Iterative Methods For Linear And Non Linear Equations by Polly(DThomas
By Polly(DThomas
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Additional info for Iterative Methods For Linear And Non Linear Equations
Example text
3. 1. Let A be an N × N matrix and let x0 , b ∈ RN be given. Then within (N + 1)/2 iterations the TFQMR iteration will either break down or terminate with the solution. 31) to obtain the following result. 2. Let A = V ΛV −1 be a nonsingular diagonalizable matrix. Assume that TFQMR does not break down or terminate with the solution for k iterations. 30).
Html. Copyright ©1995 by the Society for Industrial and Applied Mathematics. This electronic version is for personal use and may not be duplicated or distributed. html. Copyright ©1995 by the Society for Industrial and Applied Mathematics. This electronic version is for personal use and may not be duplicated or distributed. 1. The minimization property and its consequences The GMRES (Generalized Minimum RESidual) was proposed in 1986 in [167] as a Krylov subspace method for nonsymmetric systems.
15. Apply CG and PCG to solve the five-point discretization of −uxx (x, y) − uyy (x, y) + ex+y u(x, y) = 1, 0 < x, y, < 1, subject to the inhomogeneous Dirichlet boundary conditions u(x, 0) = u(x, 1) = u(1, y) = 0, u(0, y) = 1, 0 < x, y < 1. Experiment with different mesh sizes and preconditioners (Fast Poisson solver, Jacobi, and symmetric Gauss–Seidel). html. Copyright ©1995 by the Society for Industrial and Applied Mathematics. This electronic version is for personal use and may not be duplicated or distributed.