TY - JOUR
T1 - Rational interpolation through the optimal attachment of poles to the interpolating polynomial
AU - Berrut, Jean Paul
AU - Mittelmann, Hans
PY - 2000
Y1 - 2000
N2 - After recalling some pitfalls of polynomial interpolation (in particular, slopes limited by Markov's inequality) and rational interpolation (e.g., unattainable points, poles in the interpolation interval, erratic behavior of the error for small numbers of nodes), we suggest an alternative for the case when the function to be interpolated is known everywhere, not just at the nodes. The method consists in replacing the interpolating polynomial with a rational interpolant whose poles are all prescribed, written in its barycentric form as in [4], and optimizing the placement of the poles in such a way as to minimize a chosen norm of the error.
AB - After recalling some pitfalls of polynomial interpolation (in particular, slopes limited by Markov's inequality) and rational interpolation (e.g., unattainable points, poles in the interpolation interval, erratic behavior of the error for small numbers of nodes), we suggest an alternative for the case when the function to be interpolated is known everywhere, not just at the nodes. The method consists in replacing the interpolating polynomial with a rational interpolant whose poles are all prescribed, written in its barycentric form as in [4], and optimizing the placement of the poles in such a way as to minimize a chosen norm of the error.
KW - Interpolation
KW - Optimal interpolation
KW - Rational interpolation
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U2 - 10.1023/A:1019168504808
DO - 10.1023/A:1019168504808
M3 - Article
AN - SCOPUS:0034390542
SN - 1017-1398
VL - 23
SP - 315
EP - 328
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 4
ER -