Background
Werschulz, Arthur Gustav was born on December 22, 1950 in Louisville. Son of Harry W. and Lee Fay (Levin) Werschulz.
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book
The Computational Complexity of Differential and Integral Equations: An Information-Based Approach (Oxford Mathematical Monographs)
(Complexity theory has become an increasingly important th...)
Complexity theory has become an increasingly important theme in mathematical research. This book deals with an approximate solution of differential or integral equations by algorithms using incomplete information. This situation often arises for equations of the form Lu = f where f is some function defined on a domain and L is a differential operator. We do not have complete information about f. For instance, we might only know its value at a finite number of points in the domain, or the values of its inner products with a finite set of known functions. Consequently the best that can be hoped for is to solve the equation to within a given accuracy at minimal cost or complexity. In this book, the theory of the complexity of the solution to differential and integral equations is developed. The relationship between the worst case setting and other (sometimes more tractable) related settings, such as the average case, probabilistic, asymptotic, and randomized settings, is also discussed. The author determines the inherent complexity of the problem and finds optimal algorithms (in the sense of having minimal cost). Furthermore, he studies to what extent standard algorithms (such as finite element methods for elliptic problems) are optimal. This approach is discussed in depth in the context of two-point boundary value problems, linear elliptic partial differential equations, integral equations, ordinary differential equations, and ill-posed problems. As a result, this volume should appeal to mathematicians and numerical analysts working on the approximate solution of differential and integral equations, as well as to complexity theorists addressing related questions in this area.
http://www.amazon.com/gp/product/0198535899/?tag=2022091-20
Complexity and Information (Lezioni Lincee)
(The twin themes of computational complexity and informati...)
The twin themes of computational complexity and information pervade this book. It starts with an introduction to information-based complexity, that is, the computational complexity of continuous mathematical models. It then moves to a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, value of information in computation, assigning values to mathematical hypotheses, and mathematical finance. The style is informal, and the goal is motivation and insight. Precise statements and proofs can be found in the monographs and papers included in the comprehensive bibliography. The book will be essential reading for researchers in the many disciplines influenced by the computational complexity of continuous problems.
http://www.amazon.com/gp/product/0521485061/?tag=2022091-20
Arthur Gustav Werschulz
Edit ProfileComputer and information sciences educator
Education
Bachelor of Science in Mathematics, Carnegie-Mellon University, 1972. Master of Science in Mathematics, Carnegie-Mellon University, 1973. Doctor of Philosophy in Mathematics, Carnegie-Mellon University, 1977.
Career
Assistant professor mathematics University Maryland Baltimore County, Catonsville, 1976-1982. Associate professor mathematics and computer science Fordham University, New York City, 1982-1991, professor mathematics and computer science, 1991-1995, professor computer science, since 1995. Visiting scholar Columbia University, New York City, 1982-1999.
Adjunct senior research scientist, since 1999.
Achievements
Works
book
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The Computational Complexity of Differential and Integral Equations: An Information-Based Approach (Oxford Mathematical Monographs)
(Complexity theory has become an increasingly important th...)
-
Complexity and Information (Lezioni Lincee)
(The twin themes of computational complexity and informati...)
-
The Computational Complexity of Differential and Integral Equations: An Information-Based Approach (Oxford Mathematical Monographs)
Connections
Married Patricia Ann Patterson, December 23, 1972. Children: Aaron, Nathaniel.
