Application of matrix polynomials to investigation of singular equations

M. V. Bulatov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: A class of matrix polynomials having some dominant properties is described, and some characteristic properties of such polynomials have been found. Reduction of integral and integro-differential equations having singular matrices at the main part to systems with nonsingular ones is proposed. For systems of nonlinear finite-dimensional equations with singular Jacobi matrix, the definition for multiplicity of a solution is introduced. Reduction methods of such systems to the systems with isolated solutions, which can be numerically solved by well-known methods, are suggested.

Keywords: matrix polynomials, differential-algebraic equations, singular integro-differential equations, singular nonlinear equations.

Submitted by: A. M. Elizarov
Received: 29.10.2005

Language: English

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