Related papers: A New Algorithm for the Inverse of Matrices with N…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
Kaltofen has proposed a new approach in [Kaltofen 1992] for computing matrix determinants. The algorithm is based on a baby steps/giant steps construction of Krylov subspaces, and computes the determinant as the constant term of a…
We consider an inverse problem of determining coefficient matrices in an $N$-system of second-order elliptic equations in a bounded two dimensional domain by a set of Cauchy data on arbitrary subboundary. The main result of the article is…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
We deepen the theory of quasiorthogonal and approximately quasiorthogonal operator algebras through an analysis of the commutative algebra case. We give a new approach to calculate the measure of orthogonality between two such subalgebras…
We develop and analyze a broad family of stochastic/randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge…
We construct explicit examples of half-sided modular inclusions ${\mathcal N}\subset{\mathcal M}$ of von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality of the relative commutant in terms…
A new determinant inequality of positive semidefinite matrices is discovered and proved by us. This new inequality is useful for attacking and solving a variety of optimization problems arising from the design of wireless communication…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…
A concise analytical formula is developed for the inverse of an invertible 3 x 3 matrix using a telescoping method, and is generalized to larger square matrices. The formula is confirmed using randomly generated matrices in Matlab
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.