Rational Krylov methods for functions of matrices with applications to fractional partial differential equations

Lidia Aceto, Daniele Bertaccini, Fabio Durastante, Paolo Novati

Type: Article

Publication Date: 2019-07-10

Citations: 23

DOI: https://doi.org/10.1016/j.jcp.2019.07.009

View Publication

Download PDF

Locations

Journal of Computational Physics - View
arXiv (Cornell University) - View - PDF
CINECA IRIS Institutial research information system (University of Pisa) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	An operational matrix based on Chelyshkov polynomials for solving multi-order fractional differential equations	2017	Y. Talaei M. Asgari
+ PDF Chat	Laguerre polynomial-based operational matrix of integration for solving fractional differential equations with non-singular kernel	2021	Chandrali Baishya P. Veeresha
+	Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection	2013	Stefan Güttel
+ PDF Chat	A New Operational Matrices-Based Spectral Method for Multi-Order Fractional Problems	2020	Muhammad Hamid Oi Mean Foong Muhammad Usman Ilyas Khan Wei Wang
+	A new approach for solving multi-variable orders differential equations with Prabhakar function	2020	Mohammadhossein Derakhshan Azim Aminataei
+	On Rational Krylov and Reduced Basis Methods for Fractional Diffusion	2021	Tobias Danczul Clemens Hofreither
+	On Rational Krylov and Reduced Basis Methods for Fractional Diffusion	2021	Tobias Danczul Clemens Hofreither
+ PDF Chat	Rational Krylov for Stieltjes matrix functions: convergence and pole selection	2020	Stefano Massei Leonardo Robol
+	NUMERICAL SOLUTION OF FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS VIA THE RATIONALIZED HAAR FUNCTIONS	2014	Yadollah Ordokhani Neda Rahimi
+ PDF Chat	A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel	2018	Dumitru Băleanu Babak Shiri H. M. Srivastava Maysaa Al Qurashi
+	Numerical solutions of fractional Riccati type differential equations by means of the Bernstein polynomials	2013	Şuayip Yüzbaşı
+	Brenstien polynomials and applications to fractional differential equa- tions	2015	Hammad Khalil Rahmat Ali Khan Mohammad Mehdi Rashidi
+ PDF Chat	Padé-type Approximations to the Resolvent of Fractional Powers of Operators	2020	Lidia Aceto Paolo Novati
+	Numerical Solution for Fractional Partial Differential Equation with Bernstein Polynomials	2014	Jinsheng Wang Liqing Liqing Liu Liu Yiming Yiming Chen Xiaohong Xiaohong Ke
+ PDF Chat	Efficient mixed rational and polynomial approximation of matrix functions	2012	Jorge Sastre
+	Padé-type approximations to the resolvent of fractional powers of operators	2019	Lidia Aceto Paolo Novati
+ PDF Chat	Numerical Solutions to Some Families of Fractional Order Differential Equations by Laguerre Polynomials	2020	Adnan Khan Kamal Shah Danfeng Luo
+ PDF Chat	Rational Laguerre Functions And Their Applications	2015	A. Aminataei S. Ahmadi Asl Z. Kalatehbojdi
+ PDF Chat	Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations	2022	Farah Suraya Md Nasrudin Chang Phang
+	HYBRID OF RATIONALIZED HAAR FUNCTIONS METHOD FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER	2016	Yadollah Ordokhani Neda Rahimi

Works That Cite This (22)

Action	Title	Year	Authors
+ PDF Chat	A unified rational Krylov method for elliptic and parabolic fractional diffusion problems	2023	Tobias Danczul Clemens Hofreither Joachim Schöberl
+ PDF Chat	Decomposing Method for Space-Time Fractional Order PDEs	2024	Ahmed Mohamed Shukur Ahmed Jaber Mohammed Rasheed Tarek Saidani
+ PDF Chat	Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis	2020	Lidia Aceto Mariarosa Mazza Stefano Serra‐Capizzano
+ PDF Chat	Padé-type Approximations to the Resolvent of Fractional Powers of Operators	2020	Lidia Aceto Paolo Novati
+ PDF Chat	Exponentially Convergent Trapezoidal Rules to Approximate Fractional Powers of Operators	2022	Lidia Aceto Paolo Novati
+	Computing functions of very large matrices with small TT/QTT ranks by quadrature formulas	2019	Daniele Bertaccini Fabio Durastante
+	On the computation of the Mittag-Leffler function of fractional powers of accretive operators	2024	Eleonora Denich Paolo Novati
+	Exponentially convergent trapezoidal rules to approximate fractional powers of operators	2021	Lidia Aceto Paolo Novati
+	Fast and accurate approximations to fractional powers of operators	2020	Lidia Aceto Paolo Novati
+	Computational aspects of the geometric mean of two matrices: a survey	2024	Dario A. Bini Bruno Iannazzo

Works Cited by This (31)

Action	Title	Year	Authors
+	EFFICIENT PRECONDITIONING FOR SEQUENCES OF PARAMETRIC COMPLEX SYMMETRIC LINEAR SYSTEMS	2004	Daniele Bertaccini
+	None	2000	Dario A. Bini Giuseppe Fiorentino
+	A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations	2014	Qianqian Yang Ian Turner Timothy J. Moroney Fawang Liu
+	Interlacing of the zeros of Jacobi polynomials with different parameters	2008	Kathy Driver Kerstin Jordaan Norbert Mbuyi
+	Discretized Fractional Calculus	1986	Ch. Lubich
+ PDF Chat	A new investigation of the extended Krylov subspace method for matrix function evaluations	2009	Leonid Knizhnerman Valeria Simoncini
+	An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations	2012	Kevin Burrage Nicholas Hale David Kay
+	Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions	1998	Vladimir Druskin Leonid Knizhnerman
+	Rational Lanczos approximations to the matrix square root and related functions	2008	Igor Moret
+	Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils	1998	Axel Ruhe