Numerical Linear Algebra and its Applications

Numerical linear algebra, also called matrix computation, has been a center of scientific and engineering computing since 1946. Most of problems in science and engineering finally become problems in matrix computations. This book gives an elementary introduction to matrix computation and it also includes some new results obtained in recent years. This book consists of nine chapters. It includes the Gaussian elimination, classical iterative methods and Krylov subspace methods for solving linear systems; the perturbation analysis of linear systems; the rounding error analysis of elimination; the orthogonal decompositions for solving linear least squares problem; and some classical methods for eigen-problems. In the last chapter, a brief survey of the latest developments in using boundary value methods for solving initial value problems of ordinary differential equations is given. This is a textbook for the senior students majoring in scientific computing and information science. It will be also useful to all who teach or study the subject.