The focus of this course will be on learning and developing stable algorithms for various matrix problems as mentioned below.
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Solving Linear systems: $LU$, $LL^T$
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Least Square and least norm problem: $QR$ decomposition
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Singular Value Decomposition: $U\Sigma V^T$
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Eigen Value Decomposition: $X\Lambda X^{-1}$
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Iterative methods: Krylov subspace methods including Lanczos, Arnoldi, Conjugate Gradient, GMRES.
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Preconditioning and structured matrix computations.
However, before we proceed with the above, we will first look at three crucial aspects that are important for any computing course. These are: