Comparing Leja and Krylov Approximations of Large Scale Matrix Exponentials
نویسندگان
چکیده
We have implemented a numerical code (ReLPM, Real Leja Points Method) for polynomial interpolation of the matrix exponential propagators exp (∆tA)v and φ(∆tA)v, φ(z) = (exp (z) − 1)/z. The ReLPM code is tested and compared with Krylov-based routines, on large scale sparse matrices arising from the spatial discretization of 2D and 3D advection-diffusion equations.
منابع مشابه
Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection∗
Matrix functions are a central topic of linear algebra, and problems of their numerical approximation appear increasingly often in scientific computing. We review various rational Krylov methods for the computation of large-scale matrix functions. Emphasis is put on the rational Arnoldi method and variants thereof, namely, the extended Krylov subspace method and the shift-and-invert Arnoldi met...
متن کاملComputational Complexity Study on Krylov Integration Factor WENO Method for High Spatial Dimension Convection-Diffusion Problems
Integration factor (IF) methods are a class of efficient time discretization methods for solving stiff problems via evaluation of an exponential function of the corresponding matrix for the stiff operator. The computational challenge in applying the methods for partial differential equations (PDEs) on high spatial dimensions (multidimensional PDEs) is how to deal with the matrix exponential for...
متن کاملLarge-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation
In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...
متن کاملKrylov single-step implicit integration factor WENO methods for advection-diffusion-reaction equations
Implicit integration factor (IIF) methods were developed in the literature for solving time-dependent stiff partial differential equations (PDEs). Recently, IIF methods are combined with weighted essentially non-oscillatory (WENO) schemes in [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368-388] to efficiently solve stiff nonlinear advection-diffusion-reaction equations. The me...
متن کاملComparing iterative methods to compute the overlap Dirac operator at nonzero chemical potential
The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present iterative Krylov subspace approximations, with deflation of critical eigenvalues, which we developed to compute the operator on large lattices. We compare the accuracy and efficiency of two alternative approximations based on the Arnoldi...
متن کامل