A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the ...

All the methods for estimating the fundamental matrix do not naturally exploit the rank-2 constraint. For these reason some few rank-2 parameterizations of the fundamental matrix have been proposed over the years. In general they can be or an over-parameterization (12 parameters) and being generally valid, or use a minimal set of parameters (eight) but do not cover all the rank-2 matrices. We p...

The mathematical problem of approximating one matrix by another of lower rank is closely related to the fundamental postulate of factor-theory. When formulated as a least-squares problem, the normal equations cannot be immediately written do~vn, since the elements of the approximate matrix are not independent of one another. The solution of the problem is simplified by first expressing the matr...

Using the tools of semiconvex duality and max-plus algebra, this work derives a new fundamental solution for the matrix differential Riccati equation (DRE) with time-varying coefficients. Such a fundamental solution, is the counterpart of the state transition matrix in linear time-varying differential equations, and can solve the DRE analytically starting with any initial condition. By parametr...

this paper presents time domain fundamental solutions for the extended biot's dynamic formulations of two-dimensional (2d) unsaturated poroelasticity. unsaturated porous media is considered as a porous media in which the voids are saturated with two immiscible fluids, i.e. liquid and gas. at first, the corresponding explicit laplace transform domain fundamental solution is obtained in term...

In computer vision, the estimation of the fundamental matrix is a basic problem that has been extensively studied. The accuracy of the estimation imposes a significant influence on subsequent tasks such as the camera trajectory determination and 3D reconstruction. In this paper we propose a new method for fundamental matrix estimation that makes use of clustering a group of 4D vectors. The key ...

Multilinear and tensor decompositions are a popular tool in linear and multilinear algebra and have a wide range of important applications to modern computing. Our paper of 1972 presented the first nontrivial application of such decompositions to fundamental matrix computations and was also a landmark in the history of the acceleration of matrix multiplication. Published in 1972 in Russian, it ...

We compare algorithms for fundamental matrix computation, which we classify into “a posteriori correction”, “internal access”, and “external access”. Doing experimental comparison, we show that the 7-parameter Levenberg-Marquardt (LM) search and the extended FNS (EFNS) exhibit the best performance and that additional bundle adjustment does not increase the accuracy to any noticeable degree.

We define a new fundamental constant associated with a P-matrix and show that this constant has various useful properties for the P-matrix linear complementarity problems (LCP). In particular, this constant is sharper than the Mathias-Pang constant in deriving perturbation bounds for the P-matrix LCP. Moreover, this new constant defines a measure of sensitivity of the solution of the P-matrix L...