Lectures in Applied Mathematics 1996; 927 pp; softcover Volume: 32 ISBN10: 0821805304 ISBN13: 9780821805305 List Price: US$160 Member Price: US$128 Order Code: LAM/32
 The lectures in this volume are the proceedings from the 1995 AMSSIAM Summer Seminar in Applied Mathematics held in Park City, UT. The mathematical theory of real number algorithms was the subject of the conference, with emphasis on geometrical, algebraic, analytic, and foundational perspectives. Investigations on efficiency played a special role. The goal of the conference was to give the topic of numerical analysis greater coherence by focusing on the mathematical side. Particular attention was aimed at strengthening the unity of mathematics and numerical analysis and narrowing the gap between pure and applied mathematics. The conference was international in character, with strong representation from the most mathematically developed parts of numerical analysis. Seminars in the following areas were held: linear algebra, nonlinear systemspath following, differential equations, linear programming, interval arithmetic, algebraic questions, foundations, information based complexity, lower bounds, and approximation theory. Readership Graduate students and research mathematicians interested in numerical analysis. Table of Contents  M. Shub  Panel discussion: Does numerical analysis need a model of computation?
 P. G. Akishin, I. V. Puzynin, and Y. S. Smirnov  On numerical solving of nonlinear Polaron equations
 E. L. Allgower and P. J. Aston  Symmetry reductions for the numerical solution of boundary value problems
 C. L. Bajaj  The combinatorics of real algebraic splines over a simplicial complex
 A. Basermann  QMR and TFQMR method for sparse nonsymmetric problems on massively parallel systems
 R. K. Beatson, G. Goodsell, and M. D. Powell  On multigrid techniques for thin plate spline interpolation in two dimensions
 M. W. Berry, B. Hendrickson, and P. Raghavan  Sparse matrix reordering schemes for browsing hypertext
 L. Blum, F. Cucker, M. Shub, and S. Smale  Algebraic settings for the problem "P \(\neq\) NP?"
 B. M. Brown, M. P. Eastham, and D. R. McCormack  A new algorithm for computing the spectral matrix for higherorder differential equations and the location of discrete eigenvalues
 J. M. Calvin  An asymptotically optimal nonadaptive algorithm for minimization of Brownian motion
 J.P. Cardinal  On two iterative methods for approximating the roots of a polynomial
 J. P. Cardinal and B. Mourrain  Algebraic approach of residues and applications
 F. Cucker and T. Lickteig  Nash trees and Nash complexity
 W. Dahmen, A. Kunoth, and R. Schneider  Operator equations, multiscale concepts and complexity
 J.P. Dedieu  Approximate solutions of numerical problems, condition number analysis and condition number theorem
 J. P. Dedieu, X. Gourdon, and J. C. Yakoubsohn  Computing the distance from a point to an algebraic hypersurface
 A. L. Dontchev  Local analysis of a Newtontype method based on partial linearization
 B. C. Eaves and U. G. Rothblum  Approximations and complexity for computing algebraic curves
 I. Z. Emiris, A. Galligo, and H. Lombardi  Numerical univariate polynomial GCD
 J. Erhel  A parallel preconditioned GMRES algorithm for sparse matrices
 K. Frank  An optimal algorithm for the local solution of integral equations
 E. Grädel and K. Meer  Descriptive complexity theory over the real numbers
 S. Heinrich  Complexity theory of Monte Carlo algorithms
 A. Iserles and A. Zanna  Qualitative numerical analysis of ordinary differential equations
 J. Ji and F. A. Potra  Tapia indicators and finite termination of infeasibleinteriorpoint methods for degenerate LCP
 A. Keller  QuasiMonte Carlo methods in computer graphics: The global illumination problem
 U. Kulisch  Numerical algorithms with automatic result verification
 T. Y. Li, T. Wang, and X. Wang  Random product homotopy with minimal BKK bound
 M. Maller and J. Whitehead  Computational complexity over the 2adic numbers
 P. Mathe  Optimal reconstruction of stochastic evolutions
 J. L. Nazareth  Lagrangian globalization: Solving nonlinear equations via constrained optimization
 A. Nemirovski  Polynomial time methods in convex programming
 V. Y. Pan  Effective parallel computations with Toeplitz and Toeplitzlike matrices filled with integers
 S. V. Pereverzev and S. G. Solodky  An efficient discretization for solving illposed problems
 L. Plaskota  Survey of computational complexity with noisy information
 D. Richardson  Lazy analysis and elementary numbers
 K. Ritter and G. W. Wasilkowski  On the average case complexity of solving Poisson equations
 J. M. Rojas  On the average number of real roots of certain random sparse polynomial systems
 M.F. Roy  Computations in real algebraic geometry
 H. Schwetlick, G. Timmermann, and R. Losche  Path following for large nonlinear equations by implicit block elimination based on recursive projections
 H. T. Siegelmann  Computability with neural networks
 A. J. Sommese and C. W. Wampler  Numerical algebraic geometry
 G. Strang  Wavelets from filter banks
 J. H. Strickland and R. S. Baty  A pragmatic overview of fast multipole methods
 V. A. Vassiliev  Topological complexity of rootfinding algorithms
 S. A. Vavasis and Y. Ye  On the relationship between layered least squares and affine scaling steps
 W. Walter  Enclosure methods for capricious solutions of ordinary differential equations
 D. S. Watkins  QRlike algorithmsAn overview of convergence theory and practice
 A. G. Werschulz  The complexity of the Poisson problem for spaces of bounded mixed derivatives
 H. Wozniakowski  Overview of informationbased complexity
