Abstract
This chapter provides a description of key algorithms used in solving problems in linear algebra, and it develops many Matlab algorithms to implement them. The efficient solution of linear equations is illustrated using the standard Matlab functions, including Gaussian elimination, and LU, QR, and Cholesky decomposition. The discussion includes consideration of symmetric, nonsymmetric, positive definite, and under- and overdetermined linear equation systems and the use of iterative and direct methods to solve these equations. The accuracy and conditioning of equation systems is examined. The least squares method is described and applications provided. Sparse matrices are introduced, and Matlab functions are used for their efficient manipulation. The matrix eigenvalue problem is defined and iterative methods for its solution are described and implemented in Matlab . Also illustrated is the use of the standard Matlab function for solving eigenvalue problems. Problems and solutions are provided.
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