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Generalization of the Nevanlinna-Pick Interpolation Problem with Multiplicities for Bounded Real Matrices

Piekarski M., Uruski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2000

Vol. 48, nr 1

49-60

This paper generalizes the interpolation problem with multiplicities to the case of tangential interpolation, i.e., there are imposed interpolation conditions on the matrix B(s) = S(s)A(s) and its deratives at the points s1,..., sn with A(s) being an arbitrary matrix and S(s) being a bounded real matrix. Assuming that the corresponding Nevanlinna-Pick matrix is positive definite, the interpolation procedure for finding a bounded real matrix which satisfies the desired interpolation condition is presented.