From quotient-difference to generalized eigenvalues and sparse polynomial interpolation
From quotient-difference to generalized eigenvalues and sparse polynomial interpolation
The numerical quotient-difference algorithm, or the qd-algorithm , can be used for determining the poles of a meromorphic function directly from its Taylor coefficients. We show that the poles computed in the qd-algorithm, regardless of their multiplicities, are converging to the solution of a generalized eigenvalue problem. In a special case when all the poles are simple, such generalized eigenvalue problem can be viewed as a reformulation of Prony's method, a method that is closely related to the Ben-Or/Tiwari algorithm for interpolating a multivariate sparse polynomial in computer algebra.
- University of Antwerp Belgium
Ben-Or/Tiwari algorithm, Prony's method, generalised eigenvalue, sparse polynomial interpolation
Ben-Or/Tiwari algorithm, Prony's method, generalised eigenvalue, sparse polynomial interpolation
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