Efficient Inversion of Matrix φ-Functions of Low Order

The paper is concerned with efficient numerical methods for solving a linear system & phi;(A)x = b, where & phi;(z) is a & phi;-function and A E RNxN. In particular in this work we are interested in the computation of & phi;(A)-1b for the case where & phi;(z) = & phi;1(z) = ez -1 z ez - 1 - z & phi;(z) = & phi;2(z) = z2 . Under suitable conditions on the spectrum of A we design fast algorithms for computing both & phi;⠃(A)-1 and & phi;⠃(A)-1b based on Newton's iteration and Krylov-type methods, respectively. Adaptations of these schemes for structured matrices are considered. In particular the cases of banded and more generally quasiseparable matrices are investigated. Numerical results are presented to show the effectiveness of our proposed algorithm

Efficient Inversion of Matrix ϕ\phi-Functions of Low Order

The paper is concerned with efficient numerical methods for solving a linear system $\phi(A) x= b$, where $\phi(z)$ is a $\phi$-function and $A\in \mathbb R^{N\times N}$. In particular in this work we are interested in the computation of ${\phi(A)}^{-1} b$ for the case where $\phi(z)=\phi_1(z)=\displaystyle\frac{e^z-1}{z}, \quad \phi(z)=\phi_2(z)=\displaystyle\frac{e^z-1-z}{z^2}$. Under suitable conditions on the spectrum of $A$ we design fast algorithms for computing both ${\phi_\ell(A)}^{-1}$ and ${\phi_\ell(A)}^{-1} b$ based on Newton's iteration and Krylov-type methods, respectively. Adaptations of these schemes for structured matrices are considered. In particular the cases of banded and more generally quasiseparable matrices are investigated. Numerical results are presented to show the effectiveness of our proposed algorithms

7th Workshop on Matrix Equations and Tensor Techniques

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Efficient Solution of Parameter Dependent Quasiseparable Systems and Computation of Meromorphic Matrix Functions

International audienceIn 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 the effectiveness of the approach

Efficient Solution of Parameter Dependent Quasiseparable Systems and Computation of Meromorphic Matrix Functions

International audienceIn 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 the effectiveness of the approach

Efficient Solution of Parameter Dependent Quasiseparable Systems and Computation of Meromorphic Matrix Functions

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