Linear Algebra
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Direct Solution Methods for Ax=b: Gaussian Elimination
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LU Decomposition for Solving Ax=b
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Jacobi Iterative Scheme for Solving Ax=b
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Eigenvector and Eigenvalue Decomposition of Matrix A
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Principal Components Analysis from Singular Value Decomposition
About Linear Systems
The solution of linear systems is one of the most basic aspects of computational science. In many applications, the solution technique often gives rise to a system of linear equations which need to be solved as efficiently as possible. In addition to Gaussian elimination, there are a host of other techniques which can be used to solve a given problem. These section offers an overview for these methods and techniques. Ultimately the goal is to solve large linear system of equations as quickly as possible. Thus consideration of the operation count is critical.