Iterative methods: Jacobi and Gauss Seidel methods

Generalised analysis Solution Step 1: Step 2: (Jacobi) Step 2: (Gauss Siedal) In a general way, Jacobi Gauss Siedal: Convergence and spectral radius Expression for error represents the exact solution. Now, taking (2) – (3) gives the error(). . Relating error with eigen value If are the eigen values of M and are the corresponding …

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Direct solvers

Direct solvers of system of algebraic equations. Gauss elimination Step 1:Making the first column zero Step 2:Making the second column elements (entries below diagonal) zero In general, kth column : Forward elimination: There are three loops in the forward elimination. Hence the order of computation is Backward substitution Algorithm for backward substitution: Here, the order …

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