Accurate and efficient matrix exponential computation

Accurate and efficient matrix exponential computation

Efficient Computation of the Matrix Exponential by Generalized Polar Decompositions

Abstract. In this paper we explore the computation of the matrix exponential in a manner that is consistent with Lie-group structure. Our point of departure is the method of generalized polar decompositions, which we modify and combine with similarity transformations that bring the underlying matrix to a form more amenable to efficient computation. We develop techniques valid for a range of Lie...

Accurate matrix exponential computation to solve coupled differential models in engineering

The matrix exponential plays a fundamental role in linear systems arising in engineering, mechanics and control theory. This work presents a new scaling-squaring algorithm for matrix exponential computation. It uses forward and backward error analysis with improved bounds for normal and nonnormal matrices. Applied to the Taylor method, it has presented a lower or similar cost compared to the st...

Fast computation of the matrix exponential for a Toeplitz matrix

The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for example as the result of discretizing integral equations with a time invariant kernel. In this case it is not obvious how to take advantage of t...

Accurate and Efficient Computation of Laplacian Spectral Distances and Kernels

This paper introduces the Laplacian spectral distances, as a function that resembles the usual distance map, but exhibits properties (e.g., smoothness, locality, invariance to shape transformations) that make them useful to processing and analyzing geometric data. Spectral distances are easily defined through a filtering of the Laplacian eigenpairs and reduce to the heat diffusion, wave, bi-har...