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The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…

Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…

We present two generalisations of Singular Value Decomposition from real-numbered matrices to dual-numbered matrices. We prove that every dual-numbered matrix has both types of SVD. Both of our generalisations are motivated by applications,…

A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…

The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…

Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…

In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally to nonlinear equality-constrained problems, called neADMM. The…

A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an…

The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…

Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissible point transformations within this class up to the…

Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…

In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…

The problem of linear equivalence for a general class of nonlinear systems, is examined throughout this paper. A relevant algorithm is developed, based on a factorization procedure. This factorization is based on the star-product, an…

Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…

The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and…

Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant…