Algebraic Systems and Computational Complexity Theory

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Significant progress has been made during the last fifteen years in the solution of nonlinear systems, particularly in computing fixed points, solving systems of nonlinear equations and applications to equilibrium models. This volume presents a self-contained account of recent work on simplicial and continuation methods applied to the solution of algebraic equations. The contents are divided into eight chapters. Chapters 1 and 2 deal with Kuhn's algorithm; Chapter 3 considers Newton's method, and a comparison ...

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1994 Hard cover BRAND NEW INSIDE/minor bumping on cover edge-No international shipping available[KS] Sewn binding. Cloth over boards. 256 p. Mathematics and Its Applications, ... 269. Audience: General/trade. Read more Show Less

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11/30/1994 Hardcover 1 Fine Media-Hardcover-Condition-Like new Pub_year-1994. Please provide street address as we ship using DHL/Fedex Express.

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11/30/1994 Hardcover 1 Fine Media-Hardcover-Condition-Like new Pub_year-1994. Please provide street address as we ship using DHL/Fedex Express.

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Overview

Significant progress has been made during the last fifteen years in the solution of nonlinear systems, particularly in computing fixed points, solving systems of nonlinear equations and applications to equilibrium models. This volume presents a self-contained account of recent work on simplicial and continuation methods applied to the solution of algebraic equations. The contents are divided into eight chapters. Chapters 1 and 2 deal with Kuhn's algorithm; Chapter 3 considers Newton's method, and a comparison between Kuhn's algorithm and Newton's method is presented in Chapter 4. The following four chapters discuss respectively, incremental algorithms and their cost theory, homotopy algorithms, zeros of polynomial mapping, and piecewise linear algorithms. For researchers and graduates interested in algebraic equations and computational complexity theory.

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For researchers and graduate students interested in computational mathematics and computer science, reports on original research into simplicial and continuation methods of solving algebraic equations. Explains a simplicial algorithm for finding the roots of a single polynomial over the complex field; contributions to error, cost, and efficiency; and simplicial homotopy algorithm for the numerical solution of systems of nonlinear algebraic equations. Also summarizes research from various disciplines on systems of algebraic equations. The CiP data shows a different title. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Preface; H.W. Kuhn. 1. Kuhn's Algorithm for Algebraic Equations. 2. Efficiency of Kuhn's Algorithm. 3. Newton Method and Approximate Zeros. 4. A Comparison of Kuhn's Algorithm and Newton Method. 5. Incremental Algorithms and their Cost Theory. 6. Homotopy Algorithms. 7. Probabilistic Discussion on Zeros of Polynomial Mappings. 9. Piecewise Linear Algorithms. References. Index.

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