Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

Matrix functions, such as the exponential, square root and cosine, play an indispensable role in various fields including quantum mechanics, control theory and numerical solution of differential ...

ABSTRACT: The iteration of one-dimensional holomorphic functions allows a definition of conductivity plateaus and charge quanta which are related to nontrivial zeros of the Riemann zeta function and ...

Abstract: We consider a generalization of the Laplace transform of Poisson shot noise defined as an integral transform with respect to a matrix exponential. We denote this as the matrix Laplace ...

Fast and differentiable implementations of matrix exponentials, Krylov exponential matrix-vector multiplications ("expmv"), KIOPS, ExpoKit functions, and more. All your exponential needs in SciML form ...

Graph Transformers (GTs) have successfully achieved state-of-the-art performance on various platforms. GTs can capture long-range information from nodes that are at large distances, unlike the local ...

In 1999, The Matrix premiered in theaters and wowed audiences across the world. It was followed by two sequels, The Matrix Reloaded and The Matrix Revolutions, in 2002 and 2003, respectively. But it ...

Abstract: A limiting property of the matrix exponential is proven: if the (1,1)-block of a 2-by-2 block matrix becomes “arbitrarily small” in a limiting process, the matrix exponential of that matrix ...

Recent work uses a simplistic approximation to the matrix exponential derivative to apply gold-standard models from evolutionary biology to a collection of challenging data analyses. Whereas one may ...

ABSTRACT: Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing ...