応用行列解析入門（テキスト） Introduction to Applied Matrix Analysis, an (Series in Contemporary Applied Mathematics)

Jin, Xiao Qing/ Vong, Seak-weng

World Scientific Publishing Co Pte Ltd（2016/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 144 p.
• 言語 ENG
• 商品コード 9789814749466
• DDC分類 512.9434

Full Description

It is well known that most problems in science and engineering eventually progress into matrix problems. This book gives an elementary introduction to applied matrix theory and it also includes some new results obtained in recent years.The book consists of eight chapters. It includes perturbation and error analysis; the conjugate gradient method for solving linear systems; preconditioning techniques; and least squares algorithms based on orthogonal transformations, etc. The last two chapters include some latest development in the area. In Chap. 7, we construct optimal preconditioners for functions of matrices. More precisely, let f be a function of matrices. Given a matrix A, there are two choices of constructing optimal preconditioners for f(A). Properties of these preconditioners are studied for different functions. In Chap. 8, we study the Bottcher-Wenzel conjecture and discuss related problems.This is a textbook for senior undergraduate or junior graduate students majoring in science and engineering. The material is accessible to students who, in various disciplines, have basic linear algebra, calculus, numerical analysis, and computing knowledge. The book is also useful to researchers in computational science who are interested in applied matrix theory.

Contents

Introduction and Review; Norms and Perturbation Analysis; Least Squares Problems; Moore-Penrose Generalized Inverse; Conjugate Gradient Method; Optimal and Superoptimal Preconditioners; Optimal Preconditioners for Functions of Matrices; Bottcher-Wenzel Conjecture and Related Problems;