Related papers: Matrix Inversion Is As Easy As Exponentiation
Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solution of the large matrix eigenvalue problems arising from…
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
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,…
On the set of mappings of the given set, we define the product of mappings. If A is associative algebra, then we consider the set of matrices, whose elements are linear mappings of algebra A. In algebra of matrices of linear mappings we…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We prove some formulas relating the inverse of a Cartan matrix with algebraic and geometric invariants of finite group representations.
This note deals with two topics of linear algebra. We give a simple and short proof of the multiplicative property of the determinant and provide a constructive formula for rotations. The derivation of the rotation matrix relies on simple…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
This study investigates tridiagonal near-Toeplitz matrices in which the Toeplitz part is strictly diagonally dominant. The focus is on determining the exact inverse of these matrices and establishing upper bounds for the infinite norms of…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
For a one-parameter family of lower triangular matrices with entries involving continuous $q$-ultraspherical polynomials we give an explicit lower triangular inverse matrix, with entries involving again continuous $q$-ultraspherical…
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…
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…
This paper studies the low-rank property of the inverse of a class of large-scale structured matrices in the tensor-train (TT) format, which is typically discretized from differential operators. An interesting question that we are concerned…
We give a combinatorial interpretation of the determinant of a matrix as a generating function over Brauer diagrams in two different but related ways. The sign of a permutation associated to its number of inversions in the Leibniz formula…
The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Equilibration scales a matrix so that the scaled matrix's row and column norms are equal. Scaling can be…
Many algorithms use data structures that maintain properties of matrices undergoing some changes. The applications are wide-ranging and include for example matchings, shortest paths, linear programming, semi-definite programming, convex…