Details
| Original language | English |
|---|---|
| Pages (from-to) | 393-408 |
| Number of pages | 16 |
| Journal | Numerische Mathematik |
| Volume | 32 |
| Issue number | 4 |
| Publication status | Published - Dec 1979 |
Abstract
In this note an ultimate generalization of Newton's classical interpolation formula is given. More precisely, we will establish the most general linear form of a Newton-like interpolation formula and a general recurrence relation for divided differences which are applicable whenever a function is to be interpolated by means of linear combinations of functions forming a Čebyšev-system such that at least one of its subsystems is again a Čebyšev-system. The theory is applied to trigonometric interpolation yielding a new algorithm which computes the interpolating trigonometric polynomial of smallest degree for any distribution of the knots by recurrence. A numerical example is given.
Keywords
- Subject Classifications: AMS(MOS), 65D05, 41A05, 42A12
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Numerische Mathematik, Vol. 32, No. 4, 12.1979, p. 393-408.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The general recurrence relation for divided differences and the general Newton-interpolation-algorithm with applications to trigonometric interpolation
AU - Mühlbach, G.
PY - 1979/12
Y1 - 1979/12
N2 - In this note an ultimate generalization of Newton's classical interpolation formula is given. More precisely, we will establish the most general linear form of a Newton-like interpolation formula and a general recurrence relation for divided differences which are applicable whenever a function is to be interpolated by means of linear combinations of functions forming a Čebyšev-system such that at least one of its subsystems is again a Čebyšev-system. The theory is applied to trigonometric interpolation yielding a new algorithm which computes the interpolating trigonometric polynomial of smallest degree for any distribution of the knots by recurrence. A numerical example is given.
AB - In this note an ultimate generalization of Newton's classical interpolation formula is given. More precisely, we will establish the most general linear form of a Newton-like interpolation formula and a general recurrence relation for divided differences which are applicable whenever a function is to be interpolated by means of linear combinations of functions forming a Čebyšev-system such that at least one of its subsystems is again a Čebyšev-system. The theory is applied to trigonometric interpolation yielding a new algorithm which computes the interpolating trigonometric polynomial of smallest degree for any distribution of the knots by recurrence. A numerical example is given.
KW - Subject Classifications: AMS(MOS), 65D05, 41A05, 42A12
UR - http://www.scopus.com/inward/record.url?scp=4243486428&partnerID=8YFLogxK
U2 - 10.1007/BF01401043
DO - 10.1007/BF01401043
M3 - Article
AN - SCOPUS:4243486428
VL - 32
SP - 393
EP - 408
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 4
ER -