V. Demichelis

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Shaun V Ault

Valdosta State University

M.M. Noor

Universiti Malaysia Pahang (UMP)

Vadim Levit

Ariel University

Jeffrey Townsend

Yale University

Alice Kozakevicius

UFSM - Universidade Federal de Santa Maria

Heron Surbakti

Universitas Sriwijaya

Sergey Konovalov

Russian Academy of Sciences 1

Angelamaria Cardone

University of Salerno

Sergey A Khaibrakhmanov

Saint-Petersburg State University

Nikos Mantzakouras

National & Kapodistrian University of Athens

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Papers by V. Demichelis

Weighted arithmetic means possessing 0 the interpolation property

by V. Demichelis and G. Allasia

Calcolo, 1988

Summary A method to construct a wide class of weighted arithmetic means, possessing the interpol... more Summary A method to construct a wide class of weighted arithmetic means, possessing the interpolation property, is proposed. The approximation problem of a continuous real function by these interpolating mean functions is examined. A few examples are given and include the Shepard formula and the classical Hermite-Fejr formula.

ON OPTIMAL NODAL SPLINES AND THEIR APPLICATIONS

... Address: Dipartimento di Matematica, Universit`a di Torino, Via Carlo Alberto 10, 10123 Torin... more

Local spline approximation methods for singular product integration

Spline Quasi‐Interpolants with Boundary Interpolation Properties for Cauchy Principal Value Integrals

We propose new quadrature rules for Cauchy principal value integrals based on quadratic spline qu... more We propose new quadrature rules for Cauchy principal value integrals based on quadratic spline quasi-interpolants, which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights and some numerical results are given.

The use of modified quasi-interpolatory splines for the solution of the Prandtl equation

Journal of Computational and Applied Mathematics, 1995

Modified quasi-interpolatory splines are used for the numerical solution of the generalized Prand... more Modified quasi-interpolatory splines are used for the numerical solution of the generalized Prandtl equation. A Nyström type method is applied, based on inserting in the integral equation a modified quasi-interpolatory spline instead of the unknown function. The integral equation can then be solved by collocation and evaluation of suitable Cauchy principal value integrals. Necessary conditions have been established for demonstrating that the approximate solution of the equation converges to the true solution.

Martensen splines and finite-part integrals

Numerical Algorithms, 2014

An algorithm for numerical integration based on quasi-interpolating splines

Numerical Algorithms, 1993

In this paper product quadratures based on quasi-interpolating splines are proposed for the numer... more

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Quasi-interpolatory splines based on Schoenberg points

Mathematics of Computation, 1996

ABSTRACT By using the Schoenberg points as quasi-interpolatory points, we achieve both generality... more ABSTRACT By using the Schoenberg points as quasi-interpolatory points, we achieve both generality and economy in contrast to previous sets, which achieve either generality or economy, but not both. The price we pay is a more com- plicated theory and weaker error bounds, although the order of convergence is unchanged. Applications to numerical integration are given and numerical examples show that the accuracy achieved, using the Schoenberg points, is comparable to that using other sets.

Spline approximation with interpolation constraints for numerical integration

International Journal of Computer Mathematics, 1999

By using a Walsh-type theorem, we impose a finite number of interpolation constraints to a polyno... more By using a Walsh-type theorem, we impose a finite number of interpolation constraints to a polynomial spline approximation operator. These constrained approximating splines reproduce polynomials and give orders of convergence identical to those of the unconstrained ones. We give an application in numerical integration by using the constrained splines for evaluation of Cauchy principal value integrals.

Uniform convergence for cauchy principal value integrals of modified quasi-interpolatory splines ∗

International Journal of Computer Mathematics, 1994

A sequence of modified quasi-interpolatory splines is introduced for numerical evaluation of Cauc... more

Numerical integration based on quasi-interpolating splines

Computing, 1993

Finite-Part Integrals and Modified Splines

BIT Numerical Mathematics, 2000

We first state a uniform convergence theorem for finite-part integrals which are derivatives of w... more We first state a uniform convergence theorem for finite-part integrals which are derivatives of weighted Cauchy principal value integrals. We then give a two-stage process to modify approximating splines and optimal nodal splines in such a way that the conditions of this theorem are satisfied. Consequently, these modified splines can be used in the numerical evaluation of these finite-part integrals. : 65D30, 65D07.

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Weighted arithmetic means possessing 0 the interpolation property

by Renata Besenghi and V. Demichelis

Calcolo, 1988

Multivariable interpolation by weighted arithmetic means at arbitrary points

by Renata Besenghi and V. Demichelis

Calcolo, 1992

... R~MARK. It is noteworthy that in Theorem 3.1 the convergence of Er to ... linear operator it ... more

Weighted arithmetic means possessing 0 the interpolation property

by V. Demichelis and G. Allasia

Calcolo, 1988

ON OPTIMAL NODAL SPLINES AND THEIR APPLICATIONS

... Address: Dipartimento di Matematica, Universit`a di Torino, Via Carlo Alberto 10, 10123 Torin... more

Local spline approximation methods for singular product integration

Spline Quasi‐Interpolants with Boundary Interpolation Properties for Cauchy Principal Value Integrals

The use of modified quasi-interpolatory splines for the solution of the Prandtl equation

Journal of Computational and Applied Mathematics, 1995

Martensen splines and finite-part integrals

Numerical Algorithms, 2014

An algorithm for numerical integration based on quasi-interpolating splines

Numerical Algorithms, 1993

In this paper product quadratures based on quasi-interpolating splines are proposed for the numer... more

Download

Quasi-interpolatory splines based on Schoenberg points

Mathematics of Computation, 1996

Spline approximation with interpolation constraints for numerical integration

International Journal of Computer Mathematics, 1999

Uniform convergence for cauchy principal value integrals of modified quasi-interpolatory splines ∗

International Journal of Computer Mathematics, 1994

A sequence of modified quasi-interpolatory splines is introduced for numerical evaluation of Cauc... more

Numerical integration based on quasi-interpolating splines

Computing, 1993

Finite-Part Integrals and Modified Splines

BIT Numerical Mathematics, 2000

Download

Weighted arithmetic means possessing 0 the interpolation property

by Renata Besenghi and V. Demichelis

Calcolo, 1988

Multivariable interpolation by weighted arithmetic means at arbitrary points

by Renata Besenghi and V. Demichelis

Calcolo, 1992

... R~MARK. It is noteworthy that in Theorem 3.1 the convergence of Er to ... linear operator it ... more

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