• # Expokit

• Referenced in 198 articles [sw00258]
• routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential ... action of a large sparse matrix exponential on an operand vector, or the solution ... Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance ... constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned...
• # MATLAB expm

• Referenced in 170 articles [sw14349]
• scaling and squaring method for the matrix exponential revisited. The scaling and squaring method ... widely used method for computing the matrix exponential, not least because it is the method ... MATLAB function expm. The method scales the matrix by a power of 2 to reduce ... computes a Padé approximant to the matrix exponential, and then repeatedly squares to undo...
• # Algorithm 919

• Referenced in 66 articles [sw07350]
• Evaluating the ϕ-Functions Appearing in Exponential Integrators. We develop an algorithm for computing ... computing the action of a certain matrix function on the vector representing the initial condition ... linear combination of the matrix exponential and other functions related to the exponential ... major computational burden in the implementation of exponential integrators, which can solve general ODEs...
• # Expint

• Referenced in 59 articles [sw07150]
• crucial for accuracy, stability, and efficiency of exponential integrators, and the approach taken here ... common approach used for computing the matrix exponential...
• # KIOPS

• Referenced in 14 articles [sw30345]
• combinations of (varphi)-functions that appear in exponential integrators. This algorithm is suitable for large ... spectrum or norm of the Jacobian matrix is known a priori. We first show that ... efficiently by computing a single exponential of a modified matrix. Then our approach ... incomplete orthogonalization procedure and project the matrix exponential on this subspace. We also present...
• # KronFit

• Referenced in 44 articles [sw20428]
• here is to use a non-standard matrix operation, the Kronecker product, to generate graphs ... exponential time. In contrast, KRONFIT takes linear time, by exploiting the structure of Kronecker matrix...
• # rstiefel

• Referenced in 23 articles [sw11607]
• rstiefel: Random orthonormal matrix generation on the Stiefel manifold. This package simulates random orthonormal matrices ... from linear and quadratic exponential family distributions on the Stiefel manifold. The most general type ... distribution covered is the matrix-variate Bingham-von Mises-Fisher distribution. Most of the simulation...
• # MIXREG

• Referenced in 5 articles [sw24547]
• Gaussian decomposition, and the diagonal matrix reparameterized using the exponential transformation. Estimation of the individual...
• # Algorithm 982

• Referenced in 2 articles [sw22551]
• variable, requires one to exponentiate only the diagonal of a matrix ... necessary to compute the exponential of a general triangular matrix. Although this work was motivated...
• # RobustDMD

• Referenced in 1 article [sw41056]
• data into a product of a matrix of exponentials, representing Fourier-like time dynamics ... matrix of coefficients, representing spatial structures. This interpretable spatio-temporal decomposition is classically formulated ... features that are not well represented by exponentials in time, the standard Frobenius norm misfit...
• # Algorithm 894

• Referenced in 3 articles [sw13925]
• computing the matrix values of ϕ-functions required in exponential integrators. The subroutines ... argument a full, diagonal, or upper quasitriangular matrix with real or complex entries...