Chemical Engineering Hand Written_Notes_Part_60

Chemical Engineering Hand Written_Notes_Part_60 - 122 3....

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122 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES (c) rounding o f each number to 3 f gures. Perform 4 iterations each by (a) Jacobi method (b) Gauss- Seidel method (c) Successive over-relaxation method with ω =1 . 5 Use initial guess x (0) = h 111 i T and compare in each case how close to the x (4) is to the exact solution. (Use 2-norm for comparison). An a ly z eth ec on v e r g en c ep r op e r t i e so fth eabo v r e ei t e r a t iv e processes using eigenvalues of the matrix ( S 1 T )ineachcase .Wh ich iteration will converge to the true solution? (16) The Jacobi iteration for a general 2 by 2 matrix has A = " ab cd # ; D = " a 0 0 d # If A is symmetric positive de f nite, f nd the eigenvalues of J = S 1 T = D 1 ( D A ) and show that Jacobi iterations converge. (17) It is desired to solve Ax = b using Jacobi and Gauss-Seidel iteration scheme where A = 421 153 247 ; A = 12 2 221 ; A = 71 23 18 13 21 51 10 1 3 Will the Jacobi and Gauss-Seidel the iterations converge? Justify
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Chemical Engineering Hand Written_Notes_Part_60 - 122 3....

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