Abstract
Numerical algorithms with complexityO(n 2) operations are proposed for solving matrix Nehari and Nehari-Takagi problems withn interpolation points. The algorithms are based on explicit formulas for the solutions and on theorems about cascade decomposition of rational matrix function given in a state space form. The method suggests also fast algorithms for LDU factorizations of structured matrices. The numerical behavior of the designed algorithms is studied for a wide set of examples.
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Gohberg, I., Olshevsky, V. Fast state space algorithms for matrix Nehari and Nehari-Takagi interpolation problems. Integr equ oper theory 20, 44–83 (1994). https://doi.org/10.1007/BF01194749
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DOI: https://doi.org/10.1007/BF01194749