Mathematics of Computation, 1943-1993: A Half-Century of Computational Mathematics - Mathematics of Computation 50th Anniversary Symposium August 9-13, 1993 Vancouver, British Columbia

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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.

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Editorial Reviews

Booknews
Proceedings of an International Conference held in Vancouver, B.C., August 1993, to commemorate the 50th anniversary of the founding of the journal Mathematics of Computation. It consisted of a Symposium on Numerical Analysis and a Minisymposium of Computational Number Theory. This proceedings contains 14 invited papers, including two not presented at the conference--an historical essay on integer factorization, and a paper on componentwise perturbation bounds in linear algebra. The invited papers present surveys on the various subdisciplines covered by Mathematics of Computation, in a historical perspective and in a language accessible to a wide audience. The 46 contributed papers address contemporary specialized work. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Preface
Mathematics of Computation: A brief history
On the development of multigrid methods and their analysis 5
An introduction to inverse problems 21
Algorithms for unconstrained optimization: A review of recent developments 33
A survey of componentwise perturbation theory in numerical linear algebra 49
Numerical evaluation of special functions 79
A survey of numerical cubature over triangles 127
New trends in the use and analysis of integral equations 151
Applications of multivariate splines 177
Initial value problems for ordinary differential equations: Development of ideas, techniques, and implementation 205
Multiresolution methods for partial differential equations 225
A comparison of techniques for solving ill-conditioned problems arising from the immersed boundary method 243
A mixed spectral-collocation and operator splitting method for the Wigner-Poisson equation 249
Finite volume methods for irregular one-dimensional grids 255
Linear rational interpolation of continuous functions over an interval 261
A von Neumann reflection for the 2-D Burgers equation 265
Slow evolution from the boundary: A new stabilizing constraint in ill-posed continuation problems 269
A finite element method for the 2D drift-diffusion semiconductor model 275
Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems 281
Error estimates for a quadrature rule for Cauchy principal value integrals 287
A numerical radius approach to stable difference schemes for parabolic systems 293
An extension of the Olver-Sookne method for the solution of second-order linear difference equations 297
The Faber polynomials for circular arcs 301
Finite element approximation for optimal control of electrically conducting fluid flows 305
ADI methods for heat equations with discontinuities along an arbitrary interface 311
Eigenvalue approximation of Fredholm integral operators 317
Spectral methods for singular perturbation problems 323
A quaternion-Jacobi method for symmetric matrices 327
On constructing Chebyshev series solutions of differential equations 333
Multiquadric collocation methods in the numerical solution of Volterra integral and integro-differential equations 337
Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations 343
Computing limiting normals to real surfaces 349
Orthogonal spline collocation solution of nonlinear Schrodinger equations 355
Who invented the computer? The debate from the viewpoint of computer architecture 361
Locking and boundary layer effects in the finite element approximation of the Reissner-Mindlin plate model 367
Efficient spectral Galerkin methods for some elliptic problems 373
Periodic solutions of higher-order difference equations in two independent variables 377
Front tracking based on high-resolution wave propagation methods 383
Time-splitting methods for nonhomogeneous conservation laws 389
Numerical aspects of uniform Airy-type asymptotic expansions 395
Local dynamics and bifurcation consistencies of continuous-time dynamical systems and their numerical discretizations 399
Computing integrals of the complex error function 403
Quadratures for improper integrals and their applications in integral equations 409
Spline harmonic analysis and wavelet bases 415
Algorithms for quadratic orders 425
Analytic computations in number theory 451
The number field sieve 465
Factoring integers before computers 481
Explicit bounds for primes in residue classes 535
Ramanujan and Euler's constant 541
Congruential sieves on FPGA computers 547
Lehmer pairs of zeros and the Riemann [xi]-function 553
A record Aliquot sequence 557
Implications of computational mathematics for the philosophy of mathematics 561
Square roots of products of algebraic numbers 567
A locally parameterized version of Lehmer's problem 573
A new method for finding amicable pairs 577
Generalized Fermat numbers 583
Evaluation of [actual symbol not reproducible] for some totally real algebraic number fields K of degree 9 589
The period of the Bell exponential integers modulo a prime 595
Computing invariant polynomials of p-adic reflection groups 599
Author Index 603
Subject Index 619
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