Le Baron Ferguson

University of California, Riverside, Mathematics, Emeritus

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Address: Lynwood, California, United States

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Universitat Autònoma de Barcelona

Columbia University

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Papers by Le Baron Ferguson

Graph allocation in static dataflow systems

ACM SIGARCH Computer Architecture News, 1986

One of the most important considerations for a dataflow multiprocessor is the algorithm by which ... more One of the most important considerations for a dataflow multiprocessor is the algorithm by which the nodes of a program graph are allocated for execution to its processors. In the case of the static type of architecture one must consider pipelining as well as spatial concurrency. This paper uses a graph partitioning scheme to aid in the design of such algorithms and selection of the associated interconnection topology. The scheme first refines the usual dataflow program graph and then partitions it into “trees.” Our study shows that the hypercube interconnection accommodates these trees in a way that allows as to develop an algorithm that places producer nodes (of a dataflow graph) nears their consumers to keep the message path very short. The algorithm achieves concurrency in simultaneous execution of subgraphs that involve parallel operations, e.g., array operations, and subgraphs that are highly iterative or recursive. An analytical model is given to evaluate the performance of t...

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Part IV. Historical notes and remarks

Mathematical Surveys and Monographs, 1980

Müntz’s theorem and integral polynomials

Mathematical Surveys and Monographs, 1980

Complex case II: Nonvoid interior

Mathematical Surveys and Monographs, 1980

Complex case I: Void interior

Mathematical Surveys and Monographs, 1980

Čebyšev Polynomials and Transfinite Diameter

Mathematical Surveys and Monographs, 1980

Uniform approximation by polynomials with integral coefficients. II

Pacific Journal of Mathematics, 1968

Let A be a discrete subring of C of rank 2. Let X be a compact subset of C with transfinite diame... more Let A be a discrete subring of C of rank 2. Let X be a compact subset of C with transfinite diameter not less than unity or with transfinite diameter less than unity, void interior, and connected complement. In an earlier paper we characterized the complex valued functions on X which can be uniformly approximated by elements from the ring of polynomials A[z], In this paper the same problem is studied where X is a compact subset of C with transfinite diameter d(X) less than unity and with nonvoid interior. It is also studied for certain compact subsets of C n where n is any positive integer. These subsets will have the property that every continuous function holomorphic on the interior is uniformly approximable by complex polynomials. A large class of sets of this type is shown to exist.

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An Architecture for a Dataflow Multiprocessor

Icpp, 1985

Analytic functions

Mathematical Surveys and Monographs, 1980

As usual we let R be any discrete subring of the complex numbers. Throughout this chapter R will ... more As usual we let R be any discrete subring of the complex numbers. Throughout this chapter R will always contain the identity. DEFINITION 11.1. Let/be a complex valued function on a subset X of C. For each n in N set £"(/)= inf \\f-p\\ x deg/></i where the/?'s have arbitrary complex coefficients and £"<(/)= inf ||/-9H* deg q < n where the coefficients of the q's he in R. Clearly E Q {f) > E x (f) > , ES(f) > W) > , 0) and E"(f) < E< n (f), n e N. (2) In Part II we were concerned with characterizing those/for which E*(f)->0 as n-» oo. In Part III we will obtain information about the asymptotic behavior of the sequence {E*(f)} as n-> oo. From (2) we have a sort of lower bound on the rate of convergence of E*(f) to zero which we will not mention again. In the present chapter we will be concerned with the effect on the sequence {E*(f)} of the hypothesis that/be analytic. If/is analytic on an interval, then by a well-known theorem of S. N. Bernstein (Lorentz [66, 5.5]) there exists p < 1 such that E n (f) = 0(p n), i.e., there exists a constant C such that E n (f) < Cp n , all n in N. A similar result holds for E%(f). We start with the following. THEOREM 11.2. Let q be a monic polynomial in R[z], 0 < p, < p 2 , and z v. .. , z k the zeros of q. If f is analytic where \q{z)\ < p 2 and X = (z: \q(z)\ < pj}, then E£(f) = 0(p n) on X for some p < \ if and only if for every positive integer r there is a polynomial q r in R [z] satisfying tf\zj) = f (*\zj), \<j<k,0<s<r.

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Miscellaneous results

Mathematical Surveys and Monographs, 1980

Adelic case

Mathematical Surveys and Monographs, 1980

Real case

Mathematical Surveys and Monographs, 1980

Algebraic kernels

Mathematical Surveys and Monographs, 1980

Discrete rings

Mathematical Surveys and Monographs, 1980

Uniform and L p approximation for generalized integral polynomials

Pacific Journal of Mathematics, 1979

Let X be a compact Hausdorff space and denote the space of all real valued continuous functions o... more Let X be a compact Hausdorff space and denote the space of all real valued continuous functions on X by C(X,R). With pointwise operations this space becomes a linear space which we norm by defining \\f\\-8up x e Z 1/0*01 whenever feC(X,R). A subset j^of C(X,R) is said to be point separating if for any two distinct points x and y in X there is an / in jr with f(x) Φf(y). Let Z[SΠ denote the ring of all polynomials in elements of ^~ which have integral coefficients. Thus an element q of Z[^~] is an element of C(X,R) with the special form Σ ••• Σ h where the α's are integers, the /'s belong to ^"and the r's are nonnegative integers. Such q are our integral polynomials. If X is a subset of ^-dimensional Euclidean space and J^~ is taken to be the set of n coordinate projections, then the elements of Z[&~] are polynomials in the usual sense.

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