Mathematics of computation, 1943-1993 : a half-century of computational mathematics : Mathematics of Computation 50th Anniversary Symposium, August 9-13, 1993, Vancouver, British Columbia / Walter Gautschi, editor.

Format:

Book

Conference/Event

Author/Creator:

Mathematics of Computation 50th Anniversary Symposium, Corporate Author.

Contributor:

Gautschi, Walter, 1927- editor.

Conference Name:

Mathematics of Computation 50th Anniversary Symposium (1993 : Vancouver, B.C.)

Mathematics of Computation 50th Anniversary Symposium

Series:

Proceedings of Symposia in Applied Mathematics Series

Proceedings of symposia in applied mathematics, 0160-7634 ; v. 48

Proceedings of symposia in applied mathematics Mathematics of computation, 1943-1993

Language:

English

Subjects (All):

Numerical analysis--Congresses.

Numerical analysis.

Number theory--Data processing--Congresses.

Number theory.

Physical Description:

1 online resource (xix, 643 p. ) ill. ;

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1994]

Language Note:

English

Summary:

This volume, containing the proceedings of an international conference commemorating the fiftieth anniversary of Mathematics of Computation, reflects the unique way in which this journal views computational mathematics as including not only numerical analysis but also computational number theory. Accordingly, the book has two parts, one for each of these two branches. The major purpose of the conference was to take stock of the current state of the field, to reflect on its recent history, and to assess future trends. This is done in substantial survey papers written by recognized experts; there are ten such surveys in the first part and four in the second. The former cover such topics as multigrid and multiresolution methods, numerical linear algebra, methods for solving differential equations, splines and their applications, optimization, and approximation methods and software for special functions. The survey papers in the second part deal with the precomputer history of integer factorization and primality testing, as well as with some of the modern techniques of factorization and with computational techniques in analytic number theory and deterministic algorithms and their complexity in algebraic number theory. A glimpse into the very active contemporary scene is provided by the forty-six short contributed papers. With extensive bibliographic references, a detailed index, and language accessible to a wide audience, this book is an authoritative resource in the field of computational mathematics.

Contents:

Intro

Contents

Preface

Mathematics of Computation: A brief history

Part I. Symposium on Numerical Analysis

Invited Papers

On the development of multigrid methods and their analysis

An introduction to inverse problems

Algorithms for unconstrained optimization: A review of recent developments

A survey of componentwise perturbation theory in numerical linear algebra

Numerical evaluation of special functions

A survey of numerical cubature over triangles

New trends in the use and analysis of integral equations

Applications of multivariate splines

Initial value problems for ordinary differential equations: Development of ideas, techniques, and implementation

Multiresolution methods for partial differential equations

Contributed Papers

A comparison of techniques for solving ill-conditioned problems arising from the immersed boundary method

A mixed spectral-collocation and operator splitting method for the Wigner-Poisson equation

Finite volume methods for irregular one-dimensional grids

Linear rational interpolation of continuous functions over an interval

A von Neumann reflection for the 2-D Burgers equation

Slow evolution from the boundary: A new stabilizing constraint in ill-posed continuation problems

A finite element method for the 2D drift-diffusion semiconductor model

Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems

Error estimates for a quadrature rule for Cauchy principal value integrals

A numerical radius approach to stable difference schemes for parabolic systems

An extension of the Olver-Sookne method for the solution of second-order linear difference equations

The Faber polynomials for circular arcs

Finite element approximation for optimal control of electrically conducting fluid flows.

ADI methods for heat equations with discontinuities along an arbitrary interface

Eigenvalue approximation of Fredholm integral operators

Spectral methods for singular perturbation problems

A quaternion-Jacobi method for symmetric matrices

On constructing Chebyshev series solutions of differential equations

Multiquadric collocation methods in the numerical solution of Volterra integral and integro-differential equations

Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations

Computing limiting normals to real surfaces

Orthogonal spline collocation solution of nonlinear Schrödinger equations

Who invented the computer? The debate from the viewpoint of computer architecture

Locking and boundary layer effects in the finite element approximation of the Reissner-Mindlin plate model

Efficient spectral Galerkin methods for some elliptic problems

Periodic solutions of higher-order difference equations in two independent variables

Front tracking based on high-resolution wave propagation methods

Time-splitting methods for nonhomogeneous conservation laws

Numerical aspects of uniform Airy-type asymptotic expansions

Local dynamics and bifurcation consistencies of continuous-time dynamical systems and their numerical discretizations

Computing integrals of the complex error function

Quadratures for improper integrals and their applications in integral equations

Spline harmonic analysis and wavelet bases

Part II. Minisymposium on Computational Number Theory

Algorithms for quadratic orders

Analytic computations in number theory

The number field sieve

Factoring integers before computers

Explicit bounds for primes in residue classes

Ramanujan and Euler's constant.

Congruential sieves on FPGA computers

Lehmer pairs of zeros and the Riemann ξ-function

A record Aliquot sequence

Implications of computational mathematics for the philosophy of mathematics

Square roots of products of algebraic numbers

A locally parameterized version of Lehmer's problem

A new method for finding amicable pairs

Generalized Fermat numbers

Evaluation of ζ[sub(k)](2) for some totally real algebraic number fields K of degree 9

The period of the Bell exponential integers modulo a prime

Computing invariant polynomials of p-adic reflection groups

Author Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and indexes.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-8218-9263-0

OCLC:

1037819690