Trigonometric interpolation and curve-fitting

Author:
A. C. R. Newbery

Journal:
Math. Comp. **24** (1970), 869-876

MSC:
Primary 65.20

DOI:
https://doi.org/10.1090/S0025-5718-1970-0279966-8

MathSciNet review:
0279966

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Some algorithms are introduced, whereby a function defined on an arbitrarily spaced set of abscissas may be interpolated or approximated by trigonometric or hyperbolic polynomials. The interpolation may be ordinary or osculatory. Least squares approximation is included; the approximant may be a pure sine series or a cosine series or a balanced trigonometric or hyperbolic polynomial. An application to a periodicity-search is described.

**[1]**A. C. R. Newbery, "Interpolation by algebraic and trigonometric polynomials,"*Math. Comp.*, v. 20, 1966, pp. 597-599. MR**34**#3752. MR**0203905 (34:3752)****[2]**P. J. Davis,*Interpolation and Approximation*, Blaisdell, Waltham, Mass., 1963. MR**28**#393. MR**0157156 (28:393)****[3]**F. B. Hildebrand,*Introduction to Numerical Analysis*, McGraw-Hill, New York, 1956. MR**17**, 788. MR**0075670 (17:788d)****[4]**F. Oliveira-Pinto, "Curve-fitting to unequally-spaced data: Polynomial and trigonometric approximation,"*Inst. Gulbenkian Ci. Centro Cálc. Ci. Estud. Program. Anál. Numér.*, No. 2, 1967, pp. 47-59. MR**37**#2408. MR**0226821 (37:2408)****[5]**G. E. Forsythe, "Generation and use of orthogonal polynomials for data fitting with a digital computer,"*J. Soc. Indust. Appl. Math.*, v. 5, 1957, pp. 74-88. MR**19**, 1079. MR**0092208 (19:1079e)****[6]**R. W. Klopfenstein, "Conditional least squares polynomial approximation,"*Math. Comp.*, v. 18, 1964, pp. 659-662. MR**29**#6611. MR**0169361 (29:6611)**

Retrieve articles in *Mathematics of Computation*
with MSC:
65.20

Retrieve articles in all journals with MSC: 65.20

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0279966-8

Keywords:
Trigonometric interpolation,
trigonometric curve-fitting,
osculatory trigonometric interpolation,
constrained trigonometric approximation,
exponential approximation,
periodicity detection,
harmonic analysis

Article copyright:
© Copyright 1970
American Mathematical Society