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Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics
Edited by: Walter Gautschi
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Proceedings of Symposia in Applied Mathematics
1995; 644 pp; hardcover
Volume: 48
ISBN-10: 0-8218-0291-7
ISBN-13: 978-0-8218-0291-5
List Price: US$110 Member Price: US$88
Order Code: PSAPM/48

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.

Numerical analysts in academia and industry, engineers, physicists, mathematical historians, computational number theorists, and cryptographers.

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"Recommended."

-- ITW Nieuws

Part I. Symposium on Numerical Analysis. Invited Papers
• J. H. Bramble -- On the development of multigrid methods and their analysis
• M. Cheney -- An introduction to inverse problems
• D. Goldfarb -- Algorithms for unconstrained optimization: A review of recent developments
• N. J. Higham -- A survey of componentwise perturbation theory in numerical linear algebra
• D. W. Lozier and F. W. J. Olver -- Numerical evaluation of special functions
• J. N. Lyness and R. Cools -- A survey of numerical cubature over triangles
• J. C. Nédélec -- New trends in the use and analysis of integral equations
• L. L. Schumaker -- Applications of multivariate splines
• H. J. Stetter -- Initial value problems for ordinary differential equations: Development of ideas, techniques, and implementation
• R. Temam -- Multiresolution methods for partial differential equations
• Contributed Papers
• L. Adams and Z. Yang -- A comparison of techniques for solving ill-conditioned problems arising from the immersed boundary method
• A. Arnold -- A mixed spectral-collocation and operator splitting method for the Wigner-Poisson equation
• M. J. Berger, R. J. LeVeque, and L. G. Stern -- Finite volume methods for irregular one-dimensional grids
• J.-P. Berrut -- Linear rational interpolation of continuous functions over an interval
• M. Brio and J. K. Hunter -- A von Neumann reflection for the 2-D Burgers equation
• A. S. Carasso -- Slow evolution from the boundary: A new stabilizing constraint in ill-posed continuation problems
• Z. Chen -- A finite element method for the 2D drift-diffusion semiconductor model
• S. De Marchi, M. Vianello, and R. Zanovello -- Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems
• K. Diethelm -- Error estimates for a quadrature rule for Cauchy principal value integrals
• M. Goldberg -- A numerical radius approach to stable difference schemes for parabolic systems
• T. Hasegawa and T. Torii -- An extension of the Olver-Sookne method for the solution of second-order linear difference equations
• M. He -- The Faber polynomials for circular arcs
• L. S. Hou and S. S. Ravindran -- Finite element approximation for optimal control of electrically conducting fluid flows
• Z. Li and A. Mayo -- ADI methods for heat equations with discontinuities along an arbitrary interface
• E. B. Lin -- Eigenvalue approximation of Fredholm integral operators
• W. Liu and T. Tang -- Spectral methods for singular perturbation problems
• N. Mackey -- A quaternion-Jacobi method for symmetric matrices
• A. J. MacLeod -- On constructing Chebyshev series solutions of differential equations
• A. Makroglou -- Multiquadric collocation methods in the numerical solution of Volterra integral and integro-differential equations
• K. J. Maschhoff -- Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations
• D. O'Shea and L. Wilson -- Computing limiting normals to real surfaces
• M. P. Robinson -- Orthogonal spline collocation solution of nonlinear Schrödinger equations
• R. Rojas -- Who invented the computer? The debate from the viewpoint of computer architecture
• C. Schwab and M. Suri -- Locking and boundary layer effects in the finite element approximation of the Reissner-Mindlin plate model
• J. Shen -- Efficient spectral Galerkin methods for some elliptic problems
• Q. Sheng and R. P. Agarwal -- Periodic solutions of higher-order difference equations in two independent variables
• K.-M. Shyue -- Front tracking based on high-resolution wave propagation methods
• T. Tang and Z.-H. Teng -- Time-splitting methods for nonhomogeneous conservation laws
• N. M. Temme -- Numerical aspects of uniform Airy-type asymptotic expansions
• X. Wang, E. K. Blum, and Q. Li -- Local dynamics and bifurcation consistencies of continuous-time dynamical systems and their numerical discretizations
• J. A. C. Weideman -- Computing integrals of the complex error function
• Y. Xu and Y. Zhao -- Quadratures for improper integrals and their applications in integral equations
• V. A. Zheludev -- Spline harmonic analysis and wavelet bases
Part II. Minisymposium on Computational Number Theory. Dedicated to the memory of Derrick Henry Lehmer. Invited papers
• I. Biehl and J. Buchmann -- Algorithms for quadratic orders
• A. M. Odlyzko -- Analytic computations in number theory
• C. Pomerance -- The number field sieve
• H. C. Williams and J. O. Shallit -- Factoring integers before computers
• Contributed Papers
• E. Bach and J. Sorenson -- Explicit bounds for primes in residue classes
• R. P. Brent -- Ramanujan and Euler's constant
• N. D. Bronson and D. A. Buell -- Congruential sieves on FPGA computers
• G. Csordas, W. Smith, and R. S. Varga -- Lehmer pairs of zeros and the Riemann $$\xi$$-function
• A. W. P. Guy and R. K. Guy -- A record Aliquot sequence
• A. J. Lazarus -- Implications of computational mathematics for the philosophy of mathematics
• P. L. Montgomery -- Square roots of products of algebraic numbers
• G. A. Ray -- A locally parameterized version of Lehmer's problem
• H. J. J. te Riele -- A new method for finding amicable pairs
• H. Riesel and A. Björn -- Generalized Fermat numbers
• K. Takeuchi -- Evaluation of $$\zeta _K(2)$$ for some totally real algebraic number fields $$K$$ of degree 9
• S. S. Wagstaff, Jr. -- The period of the Bell exponential integers modulo a prime
• C. Xu -- Computing invariant polynomials of $$p$$-adic reflection groups