POLYNOMIAL systems of equations frequently arise in solid modelling, robotics, computer vision, chemistry, chemical engineering, and mechanical engineering. Locally convergent iterative methods such as quasi-Newton methods may diverge or fail to find all meaningful solutions of a polynomial system. This paper proposes a parallel homotopy algorithm for polynomial systems of equations that is gua...

Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matri...

Positive polynomial matrices play a fundamental role in systems and control theory: they represent e.g. spectral density functions of stochastic processes and show up in spectral factorizations, robust control and filter design problems. Positive polynomials obviously form a convex set and were recently studied in the area of convex optimization [1, 5]. It was shown in [2, 5] that positive poly...

Abstract. The Amitsur-Levitski theorem asserts that Mn(F ) satisfies a polynomial identity of degree 2n. (Here, F is a field and Mn(F ) is the algebra of n × n matrices over F ). It is easy to give examples of subalgebras of Mn(F ) that do satisfy an identity of lower degree and subalgebras of Mn(F ) that satisfy no polynomial identity of degree ≤ 2n− 2. Our aim in this paper is to give a full ...

Linear Complementarity Problems (LCPs) belong to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Following our recently published ideas we generalize affine scaling and predictor-corrector interior point algorithms to solve LCPs with general matrices in EP-sense, namely, ...

We examine the problem of equivalence of discrete time auto-regressive representations (DTARRs) over a finite time interval. Two DTARRs are defined as fundamentally equivalent (FE) over a finite time interval [0, N ] if their solution spaces or behaviours are isomorphic. We generalise the concept of strict equivalence (SE) of matrix pencils to the case of general polynomial matrices and in turn...

The class of sufficient matrices is important in the study of the linear complementarity problem (LCP) — some interior point methods (IPM’s) for LCP’s with sufficient data matrices have complexity polynomial in the bit size of the matrix and its handicap. In this paper we show that the handicap of a sufficient matrix may be exponential in its bit size, implying that the known complexity bounds ...

We propose a method and algorithm for computing the weighted MoorePenrose inverse of one-variable rational matrices. Continuing this idea, we develop an algorithm for computing the weighted Moore-Penrose inverse of one-variable polynomial matrix. These methods and algorithms are generalizations of the method or computing the weighted Moore-Penrose inverse for constant matrices, originated in [2...