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Symbolic-numeric sparse interpolation of multivariate polynomials. (English) Zbl 1167.65003
Prony’s and other methods are used for symbolic interpolation using multivariate polynomials. The work includes an error analysis and an analysis of both the stability and the sensitivity of the process with the use of bounds on generalized eigenvalues. This is all for floating-point arithmetic and fixed precision. The discussions of the sensitivity and stability, as well as the conditioning of the interpolation problem, are based on probability estimates. Algorithms and examples for the application of the analysis are presented too.

MSC:
65D05 Numerical interpolation
74A05 Kinematics of deformation
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
68W30 Symbolic computation and algebraic computation
Software:
FOXBOX; mctoolbox
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