Lubachevsky, Boris D. Structure of the inverse to the Sylvester resultant matrix. (English) Zbl 0631.15015 Linear Algebra Appl. 85, 191-202 (1987). The problem of solving the equation \(ax+by=c\) where a, b and c are given and x and y unknown polynomials of \(\lambda\) of degrees m, n, \(m+n-1\), n- 1, m-1 correspondingly is intimately related to the \((m+n)\times (m+n)\) Sylvester resultant matrix S of polynomials a and b. The author finds a representation of \(S^{-1}\) (if S is regular) as a sum of \(m+n\) dyadic matrices, each of which is a rational function of zeros of a and b. The representation is especially simple if all roots of each of the polynomials a and b are distinct, in which case the representation relates to the Lagrange interpolation formula. In the general case it relates to the general Hermite polynomial interpolation formula. Reviewer: B.Reichstein MSC: 15A54 Matrices over function rings in one or more variables 15A09 Theory of matrix inversion and generalized inverses 41A05 Interpolation in approximation theory Keywords:Sylvester resultant matrix; dyadic matrices; Lagrange interpolation formula; Hermite polynomial interpolation PDFBibTeX XMLCite \textit{B. D. Lubachevsky}, Linear Algebra Appl. 85, 191--202 (1987; Zbl 0631.15015) Full Text: DOI arXiv References: [1] Davis, P. J., Interpolation and Approximation (1975), Dover: Dover New York · Zbl 0111.06003 [2] Goodwin, G. C., Adaptive Filtering Prediction and Control (1985), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J [3] Lancaster, P.; Tismenetsky, M., The Theory of Matrices (1985), Academic: Academic Orlando, Fla · Zbl 0516.15018 [4] Lang, S., Algebra (1965), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0193.34701 [5] Ralston, A., A First Course in Numerical Analysis (1965), McGraw-Hill: McGraw-Hill New York · Zbl 0139.31603 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.