Related papers: Short note on the mass matrix for Gauss-Lobatto gr…
Let x be a point in R^2 with irrational slope and let \Gamma denote the lattice SL(2,Z) acting linearly on R^2. Then, the orbit \Gamma x is dense in R^2. We give efective results on the approximation of a point y in R^2 by points of the…
In this paper a generalization of the Gram-Schmidt Algorithm is presented. Actually we provide an algorithm to construct a set of equiangular vectors with a given angle $\theta\in(0,\arccos(\frac{-1}{n-1}))$ using a set of input independent…
For a matrix ${\bf A}$ with linearly independent columns, this work studies to use its normalization $\bar{\bf A}$ and ${\bf A}$ itself to approximate its orthonormalization $\bf V$. We theoretically analyze the order of the approximation…
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…
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…
We extend the geometrical inverse approximation approach for solving linear least-squares problems. For that we focus on the minimization of $1-\cos(X(A^TA),I)$, where $A$ is a given rectangular coefficient matrix and $X$ is the approximate…
We present a new matrix-based approach to detect and correct gross errors in GPS geodetic control networks. The study is carried out by introducing a new matrix, whose entries are powers of a (real or complex) variable, which fully…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations…
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have…
We provide a matrix-based formula for the Tutte symmetric function of a graph. In particular, for any graph $G$ with a designated head and tail vertex, we describe an infinite matrix $M_G$ from which the Tutte symmetric function can be…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
We conduct a study of the aliased spectral densities of Mat\'ern covariance functions on a regular grid of points, providing clarity on the properties of a popular approximation based on stochastic partial differential equations; while…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…
It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices…
The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors, matrices, etc) into an orthonormal basis (a set of orthogonal, unit-length vectors, bi or tri dimensional matrices). The…
Extending our previous results on trans-Planckian ($Gs \gg \hbar$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b \gg…
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).…