nine chapters. It includes Gaussian elimination, classical iterative methods and Krylov subspace methods for solving linear systems; the rounding error analysis of Gaussian elimination; the perturbation analysis of linear systems; orthogonal decomositions for solving linear least squares problems; 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 also be useful to all who teach or study the subject.

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