GMRES and the minimal polynomial
Copyright policy )GMRES and the minimal polynomial
A qualitative model is presented for the convergence behaviour of GMRES for solving nonsingular systems of linear equations \(Ax=b\) in finite and infinite dimensions. If the eigenvalues of the matrix \(A\) consist of a single cluster point plus outliers then the convergence factor is bounded by the cluster radius. If the eigenvalues of \(A\) consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster.
- North Carolina Agricultural and Technical State University United States
- North Carolina State University United States
Iterative numerical methods for linear systems, convergence, minimal polynomial, eigenvalue index, superlinear convergence, GMRES, Inequalities involving eigenvalues and eigenvectors
Iterative numerical methods for linear systems, convergence, minimal polynomial, eigenvalue index, superlinear convergence, GMRES, Inequalities involving eigenvalues and eigenvectors
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