Geodesic
Application of matrix polynomials to investigation of singular equations
Lobachevskii journal of mathematics, Tome 20 (2005), pp. 17-29

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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: differential-algebraic equations, singular integro-differential equations, singular nonlinear equations.
Mots-clés : matrix polynomials 
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     author = {M. V. Bulatov},
     title = {Application of matrix polynomials to investigation of singular equations},
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     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2005_20_a1/}
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M. V. Bulatov. Application of matrix polynomials to investigation of singular equations. Lobachevskii journal of mathematics, Tome 20 (2005), pp. 17-29. http://geodesic.mathdoc.fr/item/LJM_2005_20_a1/