Related papers: How to Calculate the Exponential of Matrices
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
In this article, we consider birational equivalence of exponential matrices. In characteristic zero, we give a birational classification of exponential matrices of size $n$-by-$n$ $(n \geq 2)$, which consists of two types. And in positive…
A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
The existing methods to obtain an exact-fit polynomial does not give the resulting polynomial in its standard form, and further manipulations are needed to obtain that. The new method presented here gives the coefficients of the polynomial…
Exact methods for exponentiation of matrices of dimension $N$ can be computationally expensive in terms of execution time ($N^{3}$) and memory requirements ($N^{2}$) not to mention numerical precision issues. A type of matrix often…
We derive explicit formulas for calculating $e^A$, $\cosh{A}$, $\sinh{A}, \cos{A}$ and $\sin{A}$ for a given $2\times2$ matrix $A$. We also derive explicit formulas for $e^A$ for a given $3\times3$ matrix $A$. These formulas are expressed…
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
This article derives an equation for exponentiation that can be used for calculating exponents using a parallel computing architecture.
We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues…
A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
We present a formulation of quantum circuit diagrams based on the exponential map which provides a new way to calculate graphically with circuits. We present a sound list of rewrite rules for this formulation and demonstrate a variety of…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome and hard to compute, theoretical methods: (1) average Hamiltonian theory following…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…