Related papers: A formula for inverse matrix
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
The inverse scattering problem is studied for the matrix Sturm-Liouville equation on the line. Necessary and sufficient conditions for the scattering data are obtained.
In this paper, the inverse spectral problem is applied to the integration of a periodic Volterra chain. A generalization of the Lagrange interpolation formula has been made.
In this note, we demonstrate a method to invert some Hankel matrices explicitly by using the kernel polynomials for the related classical orthogonal polynomials.
We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…
We suggest three applications for the inverses: For the inverse Motzkin matrix we look at Hankel determinants, and counting the paths inside a horizontal band, and for the inverse Schr\"oder matrix we look at the paths inside the same band,…
A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we…
We give a convolution formula for the Tutte polynomial T_M (x,y) of a matroid M.
The inverse problem of fractional Brownian motion and other Gaussian processes with stationary increments involves inverting an infinite hermitian positively definite Toeplitz matrix (a matrix that has equal elements along its diagonals).…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
In this paper, we compose a computational algorithm for the determinant and the inverse of the n x n cyclic nonadiagonal matrix. The algorithm is suited for implementation using computer algebra systems (CAS) such as Mathematica and Maple.
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and…
In this paper, we introduce two new generalized inverses of matrices, namely, the $\bra{i}{m}$-core inverse and the $\pare{j}{m}$-core inverse. The $\bra{i}{m}$-core inverse of a complex matrix extends the notions of the core inverse…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
In this paper an exponential multiplicative formula for the R-matrix is provided for the twisted affine quantum algebras.
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals