Skip to main content

Tiziano Politi

Politecnico di Bari, DEI - Dipartimento di Ingegneria Elettrica e dell'Informazione, Faculty Member

Followers

13

Following

2

Co-author

1

Public Views

Address: Bari, Puglia, Italy

less

School of the Art Institute of Chicago

University of Zagreb

Duke University

University of Melbourne

Kansas State University

University of Cologne

Rice University

Nikos Mantzakouras

National & Kapodistrian University of Athens

ramesh kumar ayyasamy

Universiti Tunku Abdul Rahman

The University Of Jordan

Interests

Uploads

Papers by Tiziano Politi

Explicit Polar Decomposition of a Class of Arrowhead Matrices

On the Solution of Skew-Symmetric Shifted Linear Systems

Computational Science – ICCS 2006, 2006

In this paper we consider the problem of solving a sequence of linear systems with coefficient ma... more In this paper we consider the problem of solving a sequence of linear systems with coefficient matrix Aα = I + αA (or Aα = αI + A), where α is a real paramater and A is skew-symmetric matrix. We propose to solve this problem exploiting the structure of the Schur decomposition of the skew-symmetric matrix and computing the Singular Value Decomposition of a bidiagonal matrix of halved size.

Combined Color Semantics and Deep Learning for the Automatic Detection of Dolphin Dorsal Fins

Electronics, 2020

Photo-identification is a widely used non-invasive technique in biological studies for understand... more Photo-identification is a widely used non-invasive technique in biological studies for understanding if a specimen has been seen multiple times only relying on specific unique visual characteristics. This information is essential to infer knowledge about the spatial distribution, site fidelity, abundance or habitat use of a species. Today there is a large demand for algorithms that can help domain experts in the analysis of large image datasets. For this reason, it is straightforward that the problem of identify and crop the relevant portion of an image is not negligible in any photo-identification pipeline. This paper approaches the problem of automatically cropping cetaceans images with a hybrid technique based on domain analysis and deep learning. Domain knowledge is applied for proposing relevant regions with the aim of highlighting the dorsal fins, then a binary classification of fin vs. no-fin is performed by a convolutional neural network. Results obtained on real images demo...

Diamond detectors for the TOTEM timing upgrade

Journal of Instrumentation, 2017

2008 JINST 3 S08001 9.3.1 The VME and PC Front End Computers 9.3.2 The PLCs 9.3.3 The supported f... more 2008 JINST 3 S08001 9.3.1 The VME and PC Front End Computers 9.3.2 The PLCs 9.3.3 The supported fieldbuses 9.3.4 The WorldFIP fieldbus 9.3.5 The Profibus fieldbus 9.4 Servers and operator consoles 9.5 Machine timing and UTC 9.5.1 Central beam and cycle management 9.5.2 Timing generation, transmission and reception 9.5.3 UTC for LHC time stamping 9.5.4 UTC generation, transmission and reception 9.5.5 NTP time protocol 9.6 Data management 9.6.1 Offline and online data repositories 9.6.2 Electrical circuits 9.6.3 Control system configuration 9.7 Communication and software frameworks 9.7.1 FEC software framework 9.7.2 Controls Middleware 9.7.3 Device access model 9.7.4 Messaging model 9.7.5 The J2EE framework for machine control 9.7.6 The UNICOS framework for industrial controls 9.7.7 The UNICOS object model 9.8 Control room software 9.8.1 Software for LHC beam operation 9.8.2 Software requirements 9.8.3 The software development process 9.8.4 Software for LHC Industrial Systems 9.9 Services for operations 9.9.1 Analogue signals transmission 9.9.2 Alarms 9.9.3 Logging 9.9.4 Post mortem 10 Beam dumping 10.1 System and main parameters 13 LHC as an ion collider 13.1 LHC parameters for lead ions 13.1.1 Nominal ion scheme 13.1.2 Early ion scheme 13.2 Orbits and optical configurations for heavy ions 13.3 Longitudinal dynamics 13.4 Effects of nuclear interactions on the LHC and its beams 13.5 Intra-beam scattering 13.6 Synchrotron radiation from lead ions LHC machine acronyms Bibliography-vi-2008 JINST 3 S08001 Chapter 1 2008 JINST 3 S08001 2.2.7 Collective beam instabilities The interaction of the charged particles in each beam with each other via electromagnetic fields and the conducting boundaries of the vacuum system can result in collective beam instabilities. Generally speaking, the collective effects are a function of the vacuum system geometry and its surface properties. They are usually proportional to the beam currents and can therefore limit the maximum attainable beam intensities. 2.2.8 Luminosity lifetime The luminosity in the LHC is not constant over a physics run, but decays due to the degradation of intensities and emittances of the circulating beams. The main cause of the luminosity decay during nominal LHC operation is the beam loss from collisions. The initial decay time of the bunch intensity, due to this effect, is:

Exploiting Ambiguities in the Analysis of Cumulative Matching Curves for Person Re-identification

Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods, 2016

In this paper, a method to find, exploit and classify ambiguities in the results of a person re-i... more In this paper, a method to find, exploit and classify ambiguities in the results of a person re-identification (PRID) algorithm is presented. We start from the assumption that ambiguity is implicit in the classical formulation of the re-identification problem, as a specific individual may resemble one or more subjects by the color of dresses or the shape of the body. Therefore, we propose the introduction of the AMbiguity rAte in REidentification (AMARE) approach, which relates the results of a classical PRID pipeline on a specific dataset with their effectiveness in re-identification terms, exploiting the ambiguity rate (AR). As a consequence, the cumulative matching curves (CMC) used to show the results of a PRID algorithm will be filtered according to the AR. The proposed method gives a different interpretation of the output of PRID algorithms, because the CMC curves are processed, split and studied separately. Real experiments demonstrate that the separation of the results is really helpful in order to better understand the capabilities of a PRID algorithm.

A Discrete Approach for the Inverse Singular Value Problem in Some Quadratic Group

Lecture Notes in Computer Science, 2003

In this paper the solution of an inverse singular value problem is considered. First the decompos... more In this paper the solution of an inverse singular value problem is considered. First the decomposition of a real square matrix A = UΣV is introduced, where U and V are real square matrices orthogonal with respect to a particular inner product defined through a real diagonal matrix G of order n having all the elements equal to ±1, and Σ is a real diagonal matrix with nonnegative elements, called G−singular values. When G is the identity matrix this decomposition is the usual SVD and Σ is the diagonal matrix of singular values. Given a set {σ1,. .. , σn} of n real positive numbers we consider the problem to find a real matrix A having them as G−singular values. Neglecting theoretical aspects of the problem, we discuss only an algorithmic issue, trying to apply a Newton type algorithm already considered for the usual inverse singular value problem.

Explicit polar decomposition of complex matrices

Electronic Journal of Linear Algebra, 2009

In [F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2 case, ... more In [F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2 case, Linear Algebra Appl., 38:239-249, 1981], the author gives a representation for the factors of the polar decomposition of a nonsingular real square matrix of order 2. Uhlig's formulae are generalized to encompass all nonzero complex matrices of order 2 as well as all order n complex matrices with rank at least n − 1.

A Continuous Approach for the Computation of the Hyperbolic Singular Value Decomposition

In this paper a continuous approach based on the Projected Gradient Flow technique is presented i... more In this paper a continuous approach based on the Projected Gradient Flow technique is presented in order to find a generalization of the Singular Value Decomposition (SVD) of a rectangular matrix called Hyperbolic SVD. If A is a m× n real matrix with full column rank and if G is a n× n diagonal sign matrix, i.e. g ii =± 1, the Hyperbolic Singular Value Decomposition of the pair (A,G) is defined as A=UΣV, where U is orthogonal, Σ is diagonal with positive entries and V is hypernormal (or G-orthogonal), i.e. V T GV=G. In this work we use a continuous approach based on the projected gradient technique obtaining two differential systems, the first one evolving on group of orthogonal matrices and the second on the quadratic group related to G. A numerical test is reported in order to show the effectiveness of the approach.

Conservative methods for ordinary differential equations on quadratic groups

Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche

An Human Perceptive Model for Person Re-identification

Proceedings of the 10th International Conference on Computer Vision Theory and Applications, 2015

Person re-identification has increasingly become an interesting task in the computer vision field... more Person re-identification has increasingly become an interesting task in the computer vision field, especially after the well known terroristic attacks on the World Trade Center in 2001. Even if video surveillance systems exist since the early 1950s, the third generation of such systems is a relatively modern topic and refers to systems formed by multiple fixed or mobile cameras-geographically referenced or not-whose information have to be handled and processed by an intelligent system. In the last decade, researchers are focusing their attention on the person re-identification task because computers (and so video surveillance systems) can handle a huge amount of data reducing the time complexity of the algorithms. Moreover, some well known image processing techniques-i.e. background subtraction-can be embedded directly on cameras, giving modularity and flexibility to the whole system. The aim of this work is to present an appearance-based method for person re-identification that models the chromatic relationship between both different frames and different areas of the same frame. This approach has been tested against two public benchmark datasets (ViPER and ETHZ) and the experiments demonstrate that the person re-identification processing by means of intra frame relationships is robust and shows great results in terms of recognition percentage.

A Formula for the Exponential of a Real Skew-Symmetric Matrix of Order 4

In this short paper the formula of the exponential matrix eA when A is a kew-symmetric real matri... more

On the Numerical Computation of Transition Matrix pth Root

A Fortran90 Routine for the Solution of Orthogonal Differential Problems

Lecture Notes in Computer Science, 2002

Constant bit rate Video Coding based on SVD video decomposition

Proceedings of the 2007 IEEE International Conference on Virtual Environments, Human-Computer Interfaces, and Measurement Systems, VECIMS 2007, 2007

In this paper, a novel video coding technique is presented, based on the decomposition of the seq... more In this paper, a novel video coding technique is presented, based on the decomposition of the sequence spanned hyperspace in orthogonal components. Good quality video can be reconstructed at the receiver, particularly for very low bit rate applications, with low residual error and smooth appearance both in motion reconstruction and in the complete absence of crisp coding artifacts such as blocking structures, basing on a few proper selected examples of the speaker and a multidimensional interpolation algorithm. Principal component analysis exploited by singular value decomposition has been used to decompose the video sequence into eigen-images. A limited set of eigen-images is chosen to span the whole video sequence subspace. Only coefficients to be used in the interpolation procedure are transmitted along the communication channel. Preliminary results are presented for Akyio QCIF video sequence.

Schur Decomposition Methods for the Computation of Rational Matrix Functions

Lecture Notes in Computer Science, 2006

In this work we consider the problem to compute the vector y = Φm,n(A)x where Φm,n(z) is a ration... more In this work we consider the problem to compute the vector y = Φm,n(A)x where Φm,n(z) is a rational function, x is a vector and A is a matrix of order N , usually nonsymmetric. The problem arises when we need to compute the matrix function f (A), being f (z) a complex analytic function and Φm,n(z) a rational approximation of f. Hence Φm,n(A) is a approximation for f (A) cheaper to compute. We consider the problem to compute first the Schur decomposition of A then the matrix rational function exploting the partial fractions expansion. In this case it is necessary to solve a sequence of linear systems with the shifted coefficient matrix (A − zjI)y = b.

Explicit Polar Decompositions of Complex Matrices

In (F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2c ase,L... more In (F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2c ase,Linear Algebra Appl., 38:239-249, 1981), the author gives a representation for the factors of the polar decomposition of a nonsingular real square matrix of order 2. Uhlig's formulae are generalized to encompass all nonzero complex matrices of order 2 as well as all order n complex matrices with rank at least n � 1.

A Note on Estimates of Diagonal Elements of the Inverse of Diagonally Dominant Tridiagonal Matrices

In this note we show how to improve some recent upper and lower bounds for the elements of the in... more In this note we show how to improve some recent upper and lower bounds for the elements of the inverse of diagonally dominant tridiagonal matrices. In particular, a technique described by (R. Peluso, and T. Politi, Some improvements on two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Lin. Alg. Appl. Vol. 330 (2001) 1-14), is used to obtain better bounds for the diagonal elements.

On stochasticity preserving methods for the computation of the matrix pth root

Mathematics and Computers in Simulation, 2015

ABSTRACT In this paper we consider the numerical computation of the matrix pth root of stochastic... more ABSTRACT In this paper we consider the numerical computation of the matrix pth root of stochastic matrices. In particular a collection of theoretical results concerning the pth root of stochastic matrices is reported and some numerical methods are described. The aim of the paper is to highlight the properties of such methods when they are applied to numerically compute the pth root of a stochastic matrix when it is expected to be stochastic too.

Tridiagonal splittings in the conditioning and parallel solution of banded linear systems

Linear Algebra and its Applications, 1997

We study the conditioning and the parallel solution of banded linear systems of algebraic equatio... more We study the conditioning and the parallel solution of banded linear systems of algebraic equations. We propose an iterative method for solving the linear system Au = b based on a tridiagonal splitting of the real coefficient matrix A which permits the study of the conditioning and the parallel solution of banded linear systems using the theoretical results known for tridiagonal systems. Sufficient conditions for the convergence of this method are studied, and the definition of tridiagonal dominant matrices is introduced, observing that for this class of matrices the iterative method converges. When the iterative method converges, the conditioning of A may be studied using that of its tridiagonal part. Finally, we consider a parallel version of this iterative method and show some parallel numerical tests.

An upper bound for the condition number of a matrix in spectral norm

Journal of Computational and Applied Mathematics, 2002

In this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(1) (1... more In this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(1) (1995) 2) for the condition number of a matrix as a function of the determinant, the Frobenius norm and of k singular values. If no singular value is known it is possible to derive an upper bound for the condition number applying lower and upper bounds for the product of a subset of singular values.

Explicit Polar Decomposition of a Class of Arrowhead Matrices

On the Solution of Skew-Symmetric Shifted Linear Systems

Computational Science – ICCS 2006, 2006

In this paper we consider the problem of solving a sequence of linear systems with coefficient ma... more In this paper we consider the problem of solving a sequence of linear systems with coefficient matrix Aα = I + αA (or Aα = αI + A), where α is a real paramater and A is skew-symmetric matrix. We propose to solve this problem exploiting the structure of the Schur decomposition of the skew-symmetric matrix and computing the Singular Value Decomposition of a bidiagonal matrix of halved size.

Combined Color Semantics and Deep Learning for the Automatic Detection of Dolphin Dorsal Fins

Electronics, 2020

Photo-identification is a widely used non-invasive technique in biological studies for understand... more Photo-identification is a widely used non-invasive technique in biological studies for understanding if a specimen has been seen multiple times only relying on specific unique visual characteristics. This information is essential to infer knowledge about the spatial distribution, site fidelity, abundance or habitat use of a species. Today there is a large demand for algorithms that can help domain experts in the analysis of large image datasets. For this reason, it is straightforward that the problem of identify and crop the relevant portion of an image is not negligible in any photo-identification pipeline. This paper approaches the problem of automatically cropping cetaceans images with a hybrid technique based on domain analysis and deep learning. Domain knowledge is applied for proposing relevant regions with the aim of highlighting the dorsal fins, then a binary classification of fin vs. no-fin is performed by a convolutional neural network. Results obtained on real images demo...

Diamond detectors for the TOTEM timing upgrade

Journal of Instrumentation, 2017

2008 JINST 3 S08001 9.3.1 The VME and PC Front End Computers 9.3.2 The PLCs 9.3.3 The supported f... more 2008 JINST 3 S08001 9.3.1 The VME and PC Front End Computers 9.3.2 The PLCs 9.3.3 The supported fieldbuses 9.3.4 The WorldFIP fieldbus 9.3.5 The Profibus fieldbus 9.4 Servers and operator consoles 9.5 Machine timing and UTC 9.5.1 Central beam and cycle management 9.5.2 Timing generation, transmission and reception 9.5.3 UTC for LHC time stamping 9.5.4 UTC generation, transmission and reception 9.5.5 NTP time protocol 9.6 Data management 9.6.1 Offline and online data repositories 9.6.2 Electrical circuits 9.6.3 Control system configuration 9.7 Communication and software frameworks 9.7.1 FEC software framework 9.7.2 Controls Middleware 9.7.3 Device access model 9.7.4 Messaging model 9.7.5 The J2EE framework for machine control 9.7.6 The UNICOS framework for industrial controls 9.7.7 The UNICOS object model 9.8 Control room software 9.8.1 Software for LHC beam operation 9.8.2 Software requirements 9.8.3 The software development process 9.8.4 Software for LHC Industrial Systems 9.9 Services for operations 9.9.1 Analogue signals transmission 9.9.2 Alarms 9.9.3 Logging 9.9.4 Post mortem 10 Beam dumping 10.1 System and main parameters 13 LHC as an ion collider 13.1 LHC parameters for lead ions 13.1.1 Nominal ion scheme 13.1.2 Early ion scheme 13.2 Orbits and optical configurations for heavy ions 13.3 Longitudinal dynamics 13.4 Effects of nuclear interactions on the LHC and its beams 13.5 Intra-beam scattering 13.6 Synchrotron radiation from lead ions LHC machine acronyms Bibliography-vi-2008 JINST 3 S08001 Chapter 1 2008 JINST 3 S08001 2.2.7 Collective beam instabilities The interaction of the charged particles in each beam with each other via electromagnetic fields and the conducting boundaries of the vacuum system can result in collective beam instabilities. Generally speaking, the collective effects are a function of the vacuum system geometry and its surface properties. They are usually proportional to the beam currents and can therefore limit the maximum attainable beam intensities. 2.2.8 Luminosity lifetime The luminosity in the LHC is not constant over a physics run, but decays due to the degradation of intensities and emittances of the circulating beams. The main cause of the luminosity decay during nominal LHC operation is the beam loss from collisions. The initial decay time of the bunch intensity, due to this effect, is:

Exploiting Ambiguities in the Analysis of Cumulative Matching Curves for Person Re-identification

Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods, 2016

In this paper, a method to find, exploit and classify ambiguities in the results of a person re-i... more In this paper, a method to find, exploit and classify ambiguities in the results of a person re-identification (PRID) algorithm is presented. We start from the assumption that ambiguity is implicit in the classical formulation of the re-identification problem, as a specific individual may resemble one or more subjects by the color of dresses or the shape of the body. Therefore, we propose the introduction of the AMbiguity rAte in REidentification (AMARE) approach, which relates the results of a classical PRID pipeline on a specific dataset with their effectiveness in re-identification terms, exploiting the ambiguity rate (AR). As a consequence, the cumulative matching curves (CMC) used to show the results of a PRID algorithm will be filtered according to the AR. The proposed method gives a different interpretation of the output of PRID algorithms, because the CMC curves are processed, split and studied separately. Real experiments demonstrate that the separation of the results is really helpful in order to better understand the capabilities of a PRID algorithm.

A Discrete Approach for the Inverse Singular Value Problem in Some Quadratic Group

Lecture Notes in Computer Science, 2003

In this paper the solution of an inverse singular value problem is considered. First the decompos... more In this paper the solution of an inverse singular value problem is considered. First the decomposition of a real square matrix A = UΣV is introduced, where U and V are real square matrices orthogonal with respect to a particular inner product defined through a real diagonal matrix G of order n having all the elements equal to ±1, and Σ is a real diagonal matrix with nonnegative elements, called G−singular values. When G is the identity matrix this decomposition is the usual SVD and Σ is the diagonal matrix of singular values. Given a set {σ1,. .. , σn} of n real positive numbers we consider the problem to find a real matrix A having them as G−singular values. Neglecting theoretical aspects of the problem, we discuss only an algorithmic issue, trying to apply a Newton type algorithm already considered for the usual inverse singular value problem.

Explicit polar decomposition of complex matrices

Electronic Journal of Linear Algebra, 2009

In [F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2 case, ... more In [F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2 case, Linear Algebra Appl., 38:239-249, 1981], the author gives a representation for the factors of the polar decomposition of a nonsingular real square matrix of order 2. Uhlig's formulae are generalized to encompass all nonzero complex matrices of order 2 as well as all order n complex matrices with rank at least n − 1.

A Continuous Approach for the Computation of the Hyperbolic Singular Value Decomposition

In this paper a continuous approach based on the Projected Gradient Flow technique is presented i... more In this paper a continuous approach based on the Projected Gradient Flow technique is presented in order to find a generalization of the Singular Value Decomposition (SVD) of a rectangular matrix called Hyperbolic SVD. If A is a m× n real matrix with full column rank and if G is a n× n diagonal sign matrix, i.e. g ii =± 1, the Hyperbolic Singular Value Decomposition of the pair (A,G) is defined as A=UΣV, where U is orthogonal, Σ is diagonal with positive entries and V is hypernormal (or G-orthogonal), i.e. V T GV=G. In this work we use a continuous approach based on the projected gradient technique obtaining two differential systems, the first one evolving on group of orthogonal matrices and the second on the quadratic group related to G. A numerical test is reported in order to show the effectiveness of the approach.

Conservative methods for ordinary differential equations on quadratic groups

Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche

An Human Perceptive Model for Person Re-identification

Proceedings of the 10th International Conference on Computer Vision Theory and Applications, 2015

Person re-identification has increasingly become an interesting task in the computer vision field... more Person re-identification has increasingly become an interesting task in the computer vision field, especially after the well known terroristic attacks on the World Trade Center in 2001. Even if video surveillance systems exist since the early 1950s, the third generation of such systems is a relatively modern topic and refers to systems formed by multiple fixed or mobile cameras-geographically referenced or not-whose information have to be handled and processed by an intelligent system. In the last decade, researchers are focusing their attention on the person re-identification task because computers (and so video surveillance systems) can handle a huge amount of data reducing the time complexity of the algorithms. Moreover, some well known image processing techniques-i.e. background subtraction-can be embedded directly on cameras, giving modularity and flexibility to the whole system. The aim of this work is to present an appearance-based method for person re-identification that models the chromatic relationship between both different frames and different areas of the same frame. This approach has been tested against two public benchmark datasets (ViPER and ETHZ) and the experiments demonstrate that the person re-identification processing by means of intra frame relationships is robust and shows great results in terms of recognition percentage.

A Formula for the Exponential of a Real Skew-Symmetric Matrix of Order 4

In this short paper the formula of the exponential matrix eA when A is a kew-symmetric real matri... more

On the Numerical Computation of Transition Matrix pth Root

A Fortran90 Routine for the Solution of Orthogonal Differential Problems

Lecture Notes in Computer Science, 2002

Constant bit rate Video Coding based on SVD video decomposition

Proceedings of the 2007 IEEE International Conference on Virtual Environments, Human-Computer Interfaces, and Measurement Systems, VECIMS 2007, 2007

In this paper, a novel video coding technique is presented, based on the decomposition of the seq... more In this paper, a novel video coding technique is presented, based on the decomposition of the sequence spanned hyperspace in orthogonal components. Good quality video can be reconstructed at the receiver, particularly for very low bit rate applications, with low residual error and smooth appearance both in motion reconstruction and in the complete absence of crisp coding artifacts such as blocking structures, basing on a few proper selected examples of the speaker and a multidimensional interpolation algorithm. Principal component analysis exploited by singular value decomposition has been used to decompose the video sequence into eigen-images. A limited set of eigen-images is chosen to span the whole video sequence subspace. Only coefficients to be used in the interpolation procedure are transmitted along the communication channel. Preliminary results are presented for Akyio QCIF video sequence.

Schur Decomposition Methods for the Computation of Rational Matrix Functions

Lecture Notes in Computer Science, 2006

In this work we consider the problem to compute the vector y = Φm,n(A)x where Φm,n(z) is a ration... more In this work we consider the problem to compute the vector y = Φm,n(A)x where Φm,n(z) is a rational function, x is a vector and A is a matrix of order N , usually nonsymmetric. The problem arises when we need to compute the matrix function f (A), being f (z) a complex analytic function and Φm,n(z) a rational approximation of f. Hence Φm,n(A) is a approximation for f (A) cheaper to compute. We consider the problem to compute first the Schur decomposition of A then the matrix rational function exploting the partial fractions expansion. In this case it is necessary to solve a sequence of linear systems with the shifted coefficient matrix (A − zjI)y = b.

Explicit Polar Decompositions of Complex Matrices

In (F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2c ase,L... more In (F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2c ase,Linear Algebra Appl., 38:239-249, 1981), the author gives a representation for the factors of the polar decomposition of a nonsingular real square matrix of order 2. Uhlig's formulae are generalized to encompass all nonzero complex matrices of order 2 as well as all order n complex matrices with rank at least n � 1.

A Note on Estimates of Diagonal Elements of the Inverse of Diagonally Dominant Tridiagonal Matrices

In this note we show how to improve some recent upper and lower bounds for the elements of the in... more In this note we show how to improve some recent upper and lower bounds for the elements of the inverse of diagonally dominant tridiagonal matrices. In particular, a technique described by (R. Peluso, and T. Politi, Some improvements on two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Lin. Alg. Appl. Vol. 330 (2001) 1-14), is used to obtain better bounds for the diagonal elements.

On stochasticity preserving methods for the computation of the matrix pth root

Mathematics and Computers in Simulation, 2015

ABSTRACT In this paper we consider the numerical computation of the matrix pth root of stochastic... more ABSTRACT In this paper we consider the numerical computation of the matrix pth root of stochastic matrices. In particular a collection of theoretical results concerning the pth root of stochastic matrices is reported and some numerical methods are described. The aim of the paper is to highlight the properties of such methods when they are applied to numerically compute the pth root of a stochastic matrix when it is expected to be stochastic too.

Tridiagonal splittings in the conditioning and parallel solution of banded linear systems

Linear Algebra and its Applications, 1997

We study the conditioning and the parallel solution of banded linear systems of algebraic equatio... more We study the conditioning and the parallel solution of banded linear systems of algebraic equations. We propose an iterative method for solving the linear system Au = b based on a tridiagonal splitting of the real coefficient matrix A which permits the study of the conditioning and the parallel solution of banded linear systems using the theoretical results known for tridiagonal systems. Sufficient conditions for the convergence of this method are studied, and the definition of tridiagonal dominant matrices is introduced, observing that for this class of matrices the iterative method converges. When the iterative method converges, the conditioning of A may be studied using that of its tridiagonal part. Finally, we consider a parallel version of this iterative method and show some parallel numerical tests.

An upper bound for the condition number of a matrix in spectral norm

Journal of Computational and Applied Mathematics, 2002

In this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(1) (1... more In this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(1) (1995) 2) for the condition number of a matrix as a function of the determinant, the Frobenius norm and of k singular values. If no singular value is known it is possible to derive an upper bound for the condition number applying lower and upper bounds for the product of a subset of singular values.