Proceedings of Symposia in Applied Mathematics 1995; 644 pp; hardcover Volume: 48 ISBN10: 0821802917 ISBN13: 9780821802915 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 fortysix 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. Readership Numerical analysts in academia and industry, engineers, physicists, mathematical historians, computational number theorists, and cryptographers. Reviews "Recommended."  ITW Nieuws Table of Contents 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 illconditioned problems arising from the immersed boundary method
 A. Arnold  A mixed spectralcollocation and operator splitting method for the WignerPoisson equation
 M. J. Berger, R. J. LeVeque, and L. G. Stern  Finite volume methods for irregular onedimensional 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 2D Burgers equation
 A. S. Carasso  Slow evolution from the boundary: A new stabilizing constraint in illposed continuation problems
 Z. Chen  A finite element method for the 2D driftdiffusion semiconductor model
 S. De Marchi, M. Vianello, and R. Zanovello  Splitting functions and numerical analysis of WRtype 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 OlverSookne method for the solution of secondorder 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 quaternionJacobi 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 integrodifferential 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 ReissnerMindlin plate model
 J. Shen  Efficient spectral Galerkin methods for some elliptic problems
 Q. Sheng and R. P. Agarwal  Periodic solutions of higherorder difference equations in two independent variables
 K.M. Shyue  Front tracking based on highresolution wave propagation methods
 T. Tang and Z.H. Teng  Timesplitting methods for nonhomogeneous conservation laws
 N. M. Temme  Numerical aspects of uniform Airytype asymptotic expansions
 X. Wang, E. K. Blum, and Q. Li  Local dynamics and bifurcation consistencies of continuoustime 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
