Related papers: An improved method for the computation of the Moor…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors…
We present explicit formulas for Moore-Penrose inverses of some families of set inclusion matrices arising from sets, vector spaces, and designs.
We introduce a method and an algorithm for computing the weighted Moore-Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
An expression for the Moore-Penrose inverse of a matrix of the form M = XNY , where X and Y are nonsingular, has been recently established by Castro-Gonz\'alez et al. [1, Theorem 2.2]. The expression plays an essential role in developing…
We develop quaternion--native iterative methods for computing the Moore--Penrose (MP) pseudoinverse of quaternion matrices and analyze their convergence. Our starting point is a damped Newton--Schulz (NS) iteration tailored to…
Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are…
The recursive method for computing the generalized LM-inverse of a constant rectangular matrix augmented by a column vector is proposed in Udwadia and Phohomsiri (2007) [16] and [17]. The corresponding algorithm for the sequential…
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval…
We propose a method and algorithm for computing the weighted Moore-Penrose inverse of one-variable rational matrices. Continuing this idea, we develop an algorithm for computing the weighted Moore-Penrose inverse of one-variable polynomial…
The aim of this work is to characterize linear maps of inner pro\-duct infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in…
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…
The Moore-Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore-Penrose inverse can succinctly express some important geometric…
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…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…
Pseudoinverses are ubiquitous tools for handling over- and under-determined systems of equations. For computational efficiency, sparse pseudoinverses are desirable. Recently, sparse left and right pseudoinverses were introduced, using…