On two-variable rational interpolation. (English) Zbl 1238.41001
Summary: The goal of this contribution is to investigate interpolation of two-variable rational functions. The tool is the two-variable Loewner matrix, which is an extension of its single-variable counterpart. The main property of the Loewner matrix is that its rank encodes the information concerning minimal complexity interpolants. Both polynomial and generalized state-space (descriptor) realizations of interpolants are presented. Examples illustrate how two-variable rational functions can be recovered from appropriate measurements.
MSC:
| 41A05 | Interpolation in approximation theory |
Keywords:
multivariate rational interpolation; two-variable rational functions; Lagrange bases; Loewner matrix; generalized (descriptor) realizations; parametrized systems and model reductionReferences:
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