Abstract
In Chapter 9 we discuss various numerical techniques for solving problems in linear algebra. For solving systems of linear equations, we discuss the effects of roundoff error, and how partial pivoting, and iterative methods, such as the Jacobi Method and the Gauss-Seidel Method help to alleviate this problem. We also introduce the Power Method for finding eigenvalues and their corresponding eigenvectors. Finally, we present three different matrix decompositions, each having its own set of applications: the LDU Decomposition, QR Factorization, and the Singular Value Decomposition.
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