Lectures in Applied Mathematics 1990; 762 pp; softcover Volume: 26 ISBN10: 0821811312 ISBN13: 9780821811313 List Price: US$301 Member Price: US$240.80 Order Code: LAM/26
 Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMSSIAM Summer Seminar, "Computational Solution of Nonlinear Systems of Equations," held in July 1988 at Colorado State University. The aim of the book is to give a wideranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of "entrylevel" survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis. Readership Table of Contents  E. L. Allgower and K. Georg  Numerically stable homotopy methods without an extra dimension
 G. Auchmuty  Duality algorithms for smooth unconstrained optimization
 M. S. Berger  Antidotes for nonintegrability of nonlinear systems: Quasiperiodic motions
 M. S. Berger  Bifurcation into folds of infinite dimension
 S. L. Blish and J. H. Curry  On the geometry of factorization algorithms
 K. Böhmer  Defect corrections and mesh independence principle for operator equations and their discretizations
 K. Böhmer and M. Zhen  On a numerical LyapunovSchmidt method
 A. Castelo, S. De Freitas, and G. Tavares  PL approximation of manifolds and its application to implicit ODEs
 T. F. Coleman  On characterizations of superlinear convergence for constrained optimization
 J. Duvallet  Computation of solutions of twopoint boundary value problems by a simplicial homotopy algorithm
 R. E. Ewing  Computational methods for nonlinear systems of partial differential equations arising in contaminant transport in porous media
 R. Fletcher  Low storage methods for unconstrained optimization
 A. Galantai  Block ABS methods for nonlinear systems of algebraic equations
 S. Gélinas and R. Vaillancourt  Application of JuliaFatou iteration theory in dielectric spectroscopy
 K. Georg  An introduction to PL algorithms
 K. Georg and D. Zachmann  Nonlinear convection diffusion equations and Newtonlike methods
 R. B. Guenther and J. W. Lee  Convergence of the NewtonRaphson method for boundary value problems of ordinary differential equations
 P. T. Harker and J.S. Pang  A dampedNewton method for the linear complementarity problem
 A. Hoy and H. Schwetlick  ome superlinearly convergent methods for solving singular nonlinear equations
 J. K. Hunter  Numerical solutions of some nonlinear dispersive wave equations
 H. Th. Jongen  Parametric optimization: Critical points and local minima
 R. B. Kearfott  Interval arithmetic techniques in the computational solution of nonlinear systems of equations: Introduction, examples, and comparisons
 C. T. Kelley  Operator prolongation methods for nonlinear equations
 B. N. Lundberg, A. B. Poore, and B. Yang  Smooth penalty functions and continuation methods for constrained optimization
 S. McKay and J. W. Thomas  Application of the fast adaptive composite grid method to nonlinear partial differential equations
 R. Mejia  Interactive program for continuation of solutions of large systems of nonlinear equations
 H. D. Mittelmann  Nonlinear parametrized equations: New results for variational problems and inequalities
 A. P. Morgan and A. J. Sommese  Generically nonsingular polynomial continuation
 A. P. Morgan, A. J. Sommese, and C. W. Wampler  Polynomial continuation for mechanism design problems
 G. Russo  A Lagrangian method for collisional kinetic equations
 R. Schaaf and K. Schmitt  On the number of solutions of semilinear elliptic problems at resonance: Some numerical experiments
 J. Scheurle  Splitting of separatrices and chaos
 P. H. Schmidt  PL methods for constructing a numerical implicit function
 H. Schwetlick  Nonstandard scaling matrices in trust region methods
 M. W. Smiley  Numerical determination of breathers and forced oscillations of nonlinear wave equations
 M. Sun  Numerical solutions of singular stochastic control problems in bounded intervals
 W. C. Thacker  Large leastsquares problems and the need for automating the generation of adjoint codes
 H. F. Walker  Newtonlike methods for underdetermined systems
 Y. Yomdin  Sard's theorem and its improved versions in numerical analysis
 T. J. Ypma  Finite difference approximation of sparse Jacobian matrices in Newtonlike methods
 J. J. Moré  A collection of nonlinear model problems
