On computingINV block preconditionings for the conjugate gradient method
Copyright policy )On computingINV block preconditionings for the conjugate gradient method
The INV(k) and MINV(k) block preconditionings for the conjugate gradient method require generation of selected elements of the inverses of symmetric matrices of bandwidth \(2k+1\). Generalizing the previously described \(k=1\) (tridiagonal) case to \(k=2\), explicit expressions for the inverse elements of a symmetric pentadiagonal matrix in terms of Green's matrix of rank two are given. The expressions are found to be seriously ill-conditioned; hence alternative computational algorithms for the inverse elements must be used. Behavior of the \(k=1\) and \(k=2\) preconditionings are compared for some discretized elliptic partial differential equation test problems in two dimensions.
- University of California, Berkeley United States
- French Alternative Energies and Atomic Energy Commission France
- University of California, San Francisco United States
Iterative numerical methods for linear systems, Boundary value problems for second-order elliptic equations, conjugate gradient method, Numerical computation of matrix norms, conditioning, scaling, preconditionings, iterative methods, Numerical solution of discretized equations for boundary value problems involving PDEs, incomplete factorization, Green's matrix, ill-conditioned
Iterative numerical methods for linear systems, Boundary value problems for second-order elliptic equations, conjugate gradient method, Numerical computation of matrix norms, conditioning, scaling, preconditionings, iterative methods, Numerical solution of discretized equations for boundary value problems involving PDEs, incomplete factorization, Green's matrix, ill-conditioned
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