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The Mathematics of Numerical Analysis
Edited by: James Renegar, Cornell University, Ithaca, NY, Michael Shub, IBM T. J. Watson Research Center, Yorktown Heights, NY, and Steve Smale, City University of Hong Kong, Kowloon, Hong Kong

Lectures in Applied Mathematics
1996; 927 pp; softcover
Volume: 32
ISBN-10: 0-8218-0530-4
ISBN-13: 978-0-8218-0530-5
List Price: US$160
Member Price: US$128
Order Code: LAM/32
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The lectures in this volume are the proceedings from the 1995 AMS-SIAM 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 systems-path following, differential equations, linear programming, interval arithmetic, algebraic questions, foundations, information based complexity, lower bounds, and approximation theory.


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 higher-order differential equations and the location of discrete eigenvalues
  • J. M. Calvin -- An asymptotically optimal non-adaptive 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 Newton-type 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 infeasible-interior-point methods for degenerate LCP
  • A. Keller -- Quasi-Monte 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 2-adic 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 Toeplitz-like matrices filled with integers
  • S. V. Pereverzev and S. G. Solodky -- An efficient discretization for solving ill-posed 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 root-finding 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 -- QR-like algorithms--An 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 information-based complexity
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