# Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics

### About this Title

**Walter Gautschi**, *Purdue University*, Editor

Publication: Proceedings of Symposia in Applied Mathematics

Publication Year:
1995; Volume 48

ISBNs: 978-0-8218-0291-5 (print); 978-0-8218-9263-3 (online)

DOI: https://doi.org/10.1090/psapm/048

### Table of Contents

**Front/Back Matter**

**Part I. Symposium on numerical analysis **

**Invited papers **

- James H. Bramble – On the development of multigrid methods and their analysis [MR 1314840]
- Margaret Cheney – An introduction to inverse problems [MR 1314841]
- Donald Goldfarb – Algorithms for unconstrained optimization: a review of recent developments [MR 1314842]
- Nicholas J. Higham – A survey of componentwise perturbation theory in numerical linear algebra [MR 1314843]
- D. W. Lozier and F. W. J. Olver – Numerical evaluation of special functions [MR 1314844]
- J. N. Lyness and Ronald Cools – A survey of numerical cubature over triangles [MR 1314845]
- J.-C. Nédélec – New trends in the use and analysis of integral equations [MR 1314846]
- Larry L. Schumaker – Applications of multivariate splines [MR 1314847]
- Hans J. Stetter – Initial value problems for ordinary differential equations: development of ideas, techniques, and implementation [MR 1314848]
- Roger Temam – Multiresolution methods for partial differential equations [MR 1314849]

**Contributed papers **

- Loyce Adams and Zhiyun Yang – A comparison of techniques for solving ill-conditioned problems arising from the immersed boundary method [MR 1314850]
- Anton 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 [MR 1314852]
- Jean-Paul Berrut – Linear rational interpolation of continuous functions over an interval [MR 1314853]
- M. Brio and J. K. Hunter – A von Neumann reflection for the $2$-D Burgers equation [MR 1314854]
- Alfred S. Carasso – Slow evolution from the boundary: A new stabilizing constraint on ill-posed continuation problems
- Zhangxin Chen – A finite element method for the 2D drift-diffusion semiconductor model [MR 1314856]
- S. De Marchi, M. Vianello and R. Zanovello – Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems [MR 1314857]
- Kai Diethelm – Error estimates for a quadrature rule for Cauchy principal value integrals [MR 1314858]
- Moshe Goldberg – A numerical radius approach to stable difference schemes for parabolic systems [MR 1314859]
- Takemitsu Hasegawa and Tatsuo Torii – An extension of the Olver-Sookne method for the solution of second-order linear difference equations [MR 1314860]
- Matthew He – The Faber polynomials for circular arcs [MR 1314861]
- L. S. Hou and S. S. Ravindran – Finite element approximation for optimal control of electrically conducting fluid flows [MR 1314862]
- Zhi Lin Li and Anita Mayo – ADI methods for heat equations with discontinuities along an arbitrary interface [MR 1314863]
- E. B. Lin – Eigenvalue approximation of Fredholm integral operators [MR 1314864]
- Wen Bin Liu and T. Tang – Spectral methods for singular perturbation problems [MR 1314865]
- Niloufer Mackey – A quaternion-Jacobi method for symmetric matrices [MR 1314866]
- Allan J. MacLeod – On constructing Chebyshev series solutions of differential equations [MR 1314867]
- Athena Makroglou – Multiquadric collocation methods in the numerical solution of Volterra integral and integro-differential equations [MR 1314868]
- Kristyn J. Maschhoff – Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations
- Donal O’Shea and Les Wilson – Computing limiting normals to real surfaces [MR 1314869]
- Mark P. Robinson – Orthogonal spline collocation solution of nonlinear Schrödinger equations [MR 1314870]
- Raúl Rojas – Who invented the computer? The debate from the viewpoint of computer architecture [MR 1314871]
- Christoph Schwab and Manil Suri – Locking and boundary layer effects in the finite element approximation of the Reissner-Mindlin plate model [MR 1314872]
- Jie Shen – Efficient spectral Galerkin methods for some elliptic problems [MR 1314873]
- Qin Sheng and Ravi P. Agarwal – Periodic solutions of higher-order difference equations in two independent variables [MR 1314874]
- Keh Ming Shyue – Front tracking based on high-resolution wave propagation methods [MR 1314875]
- T. Tang and Zhen Huan Teng – Time-splitting methods for nonhomogeneous conservation laws [MR 1314876]
- N. M. Temme – Numerical aspects of uniform Airy-type asymptotic expansions [MR 1314877]
- Xin Wang, Edward K. Blum and Qingnan Li – Local dynamics and bifurcation consistencies of continuous-time dynamical systems and their numerical discretizations [MR 1314878]
- J. A. C. Weideman – Computing integrals of the complex error function [MR 1314879]
- Yuesheng Xu and Yunhe Zhao – Quadratures for improper integrals and their applications in integral equations [MR 1314880]
- Valery A. Zheludev – Spline harmonic analysis and wavelet bases [MR 1314881]

**Minisymposium on computational number theory dedicated to the memory of
Derrick Henry Lehmer **

**Invited papers **

- Ingrid Biehl and Johannes Buchmann – Algorithms for quadratic orders [MR 1314882]
- Andrew M. Odlyzko – Analytic computations in number theory [MR 1314883]
- Carl Pomerance – The number field sieve [MR 1314884]
- H. C. Williams and J. O. Shallit – Factoring integers before computers [MR 1314885]

**Contributed papers **

- Eric Bach and Jonathan Sorenson – Explicit bounds for primes in residue classes [MR 1314886]
- Richard P. Brent – Ramanujan and Euler’s constant [MR 1314887]
- Nathan D. Bronson and Duncan A. Buell – Congruential sieves on FPGA computers [MR 1314888]
- George Csordas, Wayne Smith and Richard S. Varga – Lehmer pairs of zeros and the Riemann $\xi $-function [MR 1314889]
- Andrew W. P. Guy and Richard K. Guy – A record aliquot sequence [MR 1314890]
- Andrew J. Lazarus – Implications of computational mathematics for the philosophy of mathematics [MR 1314891]
- Peter L. Montgomery – Square roots of products of algebraic numbers [MR 1314892]
- Gary A. Ray – A locally parameterized version of Lehmer’s problem [MR 1314893]
- H. J. J. te Riele – A new method for finding amicable pairs [MR 1314894]
- Hans Riesel and Anders Björn – Generalized Fermat numbers [MR 1314895]
- Kisao Takeuchi – Evaluation of $\zeta _K(2)$ for some totally real algebraic number fields $K$ of degree $9$ [MR 1314896]
- Samuel S. Wagstaff, Jr. – The period of the Bell exponential integers modulo a prime [MR 1314897]
- Changsheng Xu – Computing invariant polynomials of $p$-adic reflection groups [MR 1314898]