a. Make an Algorithm for solving systems of linear algebraic equations using the methods below: – Gauss elimination – Gauss-Jordan – LU decomposition methods 1. Doolittle’s decomposition 2. Crout’s decomposition 3. Cholesky’s decomposition – Iterative methods 1. Gauss-Jacobi 2. Gauss-Seidel 3. Successive Relaxation 4. Conjugate Gradient
a. Make an
– Gauss elimination
– Gauss-Jordan
– LU decomposition methods
1. Doolittle’s decomposition
2. Crout’s decomposition
3. Cholesky’s decomposition
– Iterative methods
1. Gauss-Jacobi
2. Gauss-Seidel
3. Successive Relaxation
4. Conjugate Gradient
b. Write a program for solving the system Ax = b by
– Gaussian elimination algorithm
– LU decomposition methods (one of the three)
1. Doolittle’s decomposition
2. Crout’s decomposition
3. Cholesky’s decomposition
– Iterative methods (one of the two). Use x(0) = 0, ε = 10− 6.
1. Successive Overrelaxation (with some choice of ω, you can experiment with it)
2. Conjugate Gradient
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