計算線性代數導論   (91年度 下學期)

Direct Methods for Solving Linear Systems: Linear algebra on linear systems of equations, pivoting, matrix inversion, determinant, matrix factorizations, special matrices. Iterative Techniques in Matrix Algebra: Norms of vectors and matrices, eigenvalues and eigenvectors, iterative methods, error bounds, the Conjugate Gradient method. Approximating Eigenvalues: Linear algebra on eigenvalues, the power method, Householder's method, the QR algorithm. Numerical Solution of Nonlinear Systems of Equations: Fixed points for functions of several variables, Newton and Quasi-Newton methods, steepest descent techniques, homotopy methods. Approximation Theory: least squares approximation, Chebyshev and orthogonal polynomials, rational function and trigonometric approximations, fast Fourier transform.

R. L. Burden and J. D. Faires, Numerical Analysis, 7th ed., Brooks/Cole, 2001.

作業與計算習題 60%，期中考 20%，期末考 20%