Krylov Subspace Methods for Linear Systems, Eigenvalues and Model Order Reduction

Sammanfattning: New variants of Krylov subspace methods for numerical solution of linear systems, eigenvalue, and model order reduction problems are described.

A new method to solve linear systems of equations with several right-hand sides is described. It uses the basis from a previous solution to reduce the number of matrix vector multiplications needed to solve a linear system of equations with a new right-hand side.

For eigenproblems and model order reduction the rational Krylov method is used. The rational Krylov method is an extension of the shift-and-invert Arnoldi method where several shifts (factorisations of a shifted pencil) are used to compute an orthonormal basis for a subspace. It is shown how the basis vectors can be generated in parallel. It is also shown how to create a reduced-order model of a linear dynamic system, and how to make error estimates of the Laplace domain transfer function of the reduced-order model. Further it is shown how to make a passive model of a passive RLC circuit.

AMS subject classification 65F15, 65F50, 65Y05, 65F10, 93A30, 93B40