Hermite–Birkhoff interpolation by Hermite–Birkhoff splines
1981 ◽
Vol 88
(3-4)
◽
pp. 195-201
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Keyword(s):
SynopsisWe consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points, specified by a finite incidence matrix E. Similarly the allowable discontinuities of the piecewise polynomials are specified by a finite incidence matrix F. We first find necessary conditions on (E, F) for the problem to be poised, that is to have a unique solution for any given data. The main result gives sufficient conditions on (E, F) for the problem to be poised, generalising a well-known result of Atkinson and Sharma. To this end we prove some results involving estimates of the numbers of zeros of the relevant piecewise polynomials.
1983 ◽
Vol 95
(1-2)
◽
pp. 39-57
1993 ◽
Vol 58
(2)
◽
pp. 337-348
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2019 ◽
Vol 14
(4)
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Keyword(s):
1984 ◽
Vol 27
(1)
◽
pp. 65-71
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Keyword(s):