Superfast solution of real positive definite toeplitz systems
SIAM Journal on Matrix Analysis and Applications
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
Circulant preconditioners for complex Toeplitz matrices
SIAM Journal on Numerical Analysis
Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Matrix computations (3rd ed.)
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
An interpolatory approximation of the matrix exponential based on Faber polynomials
Journal of Computational and Applied Mathematics
On a method for solving an integral equation in the displacement contact problem
Applied Mathematics and Computation
Recursive-Based PCG Methods for Toeplitz Systems with Nonnegative Generating Functions
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
SIAM Journal on Scientific Computing
The Scaling and Squaring Method for the Matrix Exponential Revisited
SIAM Journal on Matrix Analysis and Applications
Preconditioning Lanczos Approximations to the Matrix Exponential
SIAM Journal on Scientific Computing
Analysis of Projection Methods for Rational Function Approximation to the Matrix Exponential
SIAM Journal on Numerical Analysis
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
Exponential time integration and Chebychev discretisation schemes for fast pricing of options
Applied Numerical Mathematics
Stopping Criteria for Rational Matrix Functions of Hermitian and Symmetric Matrices
SIAM Journal on Scientific Computing
Acceleration Techniques for Approximating the Matrix Exponential Operator
SIAM Journal on Matrix Analysis and Applications
Error Estimates for Polynomial Krylov Approximations to Matrix Functions
SIAM Journal on Matrix Analysis and Applications
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The shift-invert Arnoldi method is employed to generate an orthonormal basis from the Krylov subspace corresponding to a real Toeplitz matrix and an initial vector. The vectors and recurrence coefficients produced by this method are exploited to approximate the Toeplitz matrix exponential. Toeplitz matrix inversion formula and rapid Toeplitz matrix-vector multiplications are utilized to lower the computational costs. For convergence analysis, a sufficient condition is established to guarantee that the error bound is independent of the norm of the matrix. Numerical results are given to demonstrate the efficiency of the method.