Details
| Original language | English |
|---|---|
| Pages (from-to) | 339-347 |
| Number of pages | 9 |
| Journal | Numerische Mathematik |
| Volume | 37 |
| Issue number | 3 |
| Publication status | Published - Oct 1981 |
Abstract
This paper deals with an algorithmic approach to the Hermite-Birkhoff-(HB)interpolation problem. More precisely, we will show that Newton's classical formula for interpolation by algebraic polynomials naturally extends to HB-interpolation. Hence almost all reasons which make Newton's method superior to just solving the system of linear equations associated with the interpolation problem may be repeated. Let us emphasize just two: Newton's formula being a biorthogonal expansion has a well known permanence property when the system of interpolation conditions grows. From Newton's formula by an elementary argument due to Cauchy an important representation of the interpolation error can be derived. All of the above extends to HB-interpolation with respect to canonical complete Čebyšev-systems and naturally associated differential operators [7]. A numerical example is given.
Keywords
- Subject Classifications: AMS(MOS): 65D05, CR: 5.13
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Numerische Mathematik, Vol. 37, No. 3, 10.1981, p. 339-347.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An algorithmic approach to Hermite-Birkhoff-interpolation
AU - Mühlbach, G.
PY - 1981/10
Y1 - 1981/10
N2 - This paper deals with an algorithmic approach to the Hermite-Birkhoff-(HB)interpolation problem. More precisely, we will show that Newton's classical formula for interpolation by algebraic polynomials naturally extends to HB-interpolation. Hence almost all reasons which make Newton's method superior to just solving the system of linear equations associated with the interpolation problem may be repeated. Let us emphasize just two: Newton's formula being a biorthogonal expansion has a well known permanence property when the system of interpolation conditions grows. From Newton's formula by an elementary argument due to Cauchy an important representation of the interpolation error can be derived. All of the above extends to HB-interpolation with respect to canonical complete Čebyšev-systems and naturally associated differential operators [7]. A numerical example is given.
AB - This paper deals with an algorithmic approach to the Hermite-Birkhoff-(HB)interpolation problem. More precisely, we will show that Newton's classical formula for interpolation by algebraic polynomials naturally extends to HB-interpolation. Hence almost all reasons which make Newton's method superior to just solving the system of linear equations associated with the interpolation problem may be repeated. Let us emphasize just two: Newton's formula being a biorthogonal expansion has a well known permanence property when the system of interpolation conditions grows. From Newton's formula by an elementary argument due to Cauchy an important representation of the interpolation error can be derived. All of the above extends to HB-interpolation with respect to canonical complete Čebyšev-systems and naturally associated differential operators [7]. A numerical example is given.
KW - Subject Classifications: AMS(MOS): 65D05, CR: 5.13
UR - http://www.scopus.com/inward/record.url?scp=34250240674&partnerID=8YFLogxK
U2 - 10.1007/BF01400313
DO - 10.1007/BF01400313
M3 - Article
AN - SCOPUS:34250240674
VL - 37
SP - 339
EP - 347
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 3
ER -