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Matrices can be augmented by adding additional columns such that a partitioning of the matrix in blocks of rows defines mutually orthogonal subspaces. This augmented system can then be solved efficiently by a sum of projections onto these…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
In this article we apply proper splittings of matrices to develop an iterative process to approximate solutions of matrix equations of the form TX = W. Moreover, by using the partial order induced by positive semidefinite matrices, we…
A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The method is then applied to the Schr\"{o}dinger equation in…
We study the time and space complexity of matrix permanents over rings and semirings.
The solvability for infinite dimensional differential algebraic equations possessing a resolvent index and a Weierstra{\ss} form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which…
A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space.
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant…
A robust, fast and accurate method for solving the Colebrook-like equations is presented. The algorithm is efficient for the whole range of parameters involved in the Colebrook equation. The computations are not more demanding than…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
Our aim is to introduce the tropical tensor product and investigate its properties. In particular we show its use for solving tropical matrix equations.
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
A fast and accurate algorithm for solving a Bernstein-Vandermonde linear system is presented. The algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of Neville…