## M. V. Bulatov

# Application of matrix polynomials to investigation of singular equations

## (*Lobachevskii Journal of Mathematics, Vol.20, pp.17-29*)

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.

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