On the Convergence of Krylov Subspace Methods for Matrix Mittag-Leffler Functions

نویسندگان

  • Igor Moret
  • Paolo Novati
چکیده

In this paper we analyze the convergence of some commonly used Krylov subspace methods for computing the action of matrix Mittag-Leffler functions. As it is well known, such functions find application in the solution of fractional differential equations. We illustrate the theoretical results by some numerical experiments.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Matrix Mittag-Leffler functions of fractional nabla calculus

In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.

متن کامل

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme  may be a good approach, particularly, the schemes in numerical linear algebra for solving ...

متن کامل

Autoconvolution equations and generalized Mittag-Leffler ‎functions

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

متن کامل

Cascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

متن کامل

Convergence of Restarted Krylov Subspace Methods for Stieltjes Functions of Matrices

To approximate f(A)b—the action of a matrix function on a vector—by a Krylov subspace method, restarts may become mandatory due to storage requirements for the Arnoldi basis or due to the growing computational complexity of evaluating f on a Hessenberg matrix of growing size. A number of restarting methods have been proposed in the literature in recent years and there has been substantial algor...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Numerical Analysis

دوره 49  شماره 

صفحات  -

تاریخ انتشار 2011