Numerical Analysis / / L. Ridgway Scott.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
• VerfasserIn: Scott, L. Ridgway,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2011]; ©2011
• Year of Publication: 2011
• Language: English
• Physical Description: 1 online resource (344 p.) :; 33 line illus. 11 tables.

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin

Table of Contents

Frontmatter -- Contents -- Preface -- Chapter One. Numerical Algorithms -- Chapter Two. Nonlinear Equations -- Chapter Three. Linear Systems -- Chapter Four. Direct Solvers -- Chapter Five. Vector Spaces -- Chapter Five. Vector Spaces -- Chapter Seven. Nonlinear Systems -- Chapter Eight. Iterative Methods -- Chapter Nine. Conjugate Gradients -- Chapter Ten. Polynomial Interpolation -- Chapter Eleven. Chebyshev and Hermite Interpolation -- Chapter Twelve. Approximation Theory -- Chapter Thirteen. Numerical Quadrature -- Chapter Fourteen. Eigenvalue Problems -- Chapter Fifteen. Eigenvalue Algorithms -- Chapter Sixteen. Ordinary Differential Equations -- Chapter Seventeen. Higher-order ODE Discretization Methods -- Chapter Eighteen. Floating Point -- Chapter Nineteen. Notation -- Bibliography -- Index