Efficient Solution of Parameter Dependent Quasiseparable Systems and Computation of Meromorphic Matrix Functions
For researchers working with structured matrices, this provides a fast and robust method for solving quasiseparable systems and computing matrix functions, though it is an incremental improvement over existing techniques.
The paper proposes an efficient algorithm for solving shifted quasiseparable systems and parameter-dependent matrix equations, leveraging the invariance of quasiseparable structure under shifting and inversion. The method is applied to compute matrix functions, with numerical experiments demonstrating speed and robustness.
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the quasiseparable structure under diagonal shifting and inversion. This algorithm is applied to compute various functions of matrices. Numerical experiments show that this approach is fast and numerically robust.