A Direct Method for Chebyshev Approximation by Rational Functions

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A Direct Method for Chebyshev Approximation by Rational Functions

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Journal of the ACM (JACM) archive
Volume 11 , Issue 1 (January 1964) table of contents

Pages: 59 - 69

Year of Publication: 1964

ISSN:0004-5411

Author

Josef Stoer

Mathematisches Institut der Téchischen Hochschule München, Germany

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 4, Downloads (12 Months): 37, Citation Count: 2

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	ACHIESR, N. I. Vorlesungen iiber Approximationstheorie. Akademieverlag Berlin, 1953.
	2	W. Fraser , J. F. Hart, On the computation of rational approximations to continuous functions, Communications of the ACM, v.5 n.7, p.401-403, July 1962 [doi>10.1145/368273.368578]
	3	MXEHLY, H. J. First interim progress report on rational approximation. Off. Nay. Research, Project NR 044--196, Princeton, 1958.
	4	MAEHLY, H. J., AND WITZGALL, C. Tschebyscheff-Approximationen in kleinen Intervallen I. Approximation durch Polynome. Num. Math. 2 (1960), 142--150.
	5	Hans J. Maehly, Methods for Fitting Rational Approximations, Parts II and III, Journal of the ACM (JACM), v.10 n.3, p.257-277, July 1963 [doi>10.1145/321172.321173]
	6	MIARDVS, G., AND STRAUR, H.-D. Uber die Approximation von Funktionen bei der Aufstellung von Unterprogrammen. Elektron. Datenver. IP (1961), 180--187.
	7	MILLE, W. E. Numerical Calculus. Princeton University Press, 1949.
	8	MURNAGHN, F. D., AND WNCH, J. W. The approximation of differentiable functions by polynomials. David Taylor Model Basin Report 1175, 1958.
	9	AND . The determination of the Chebyshev approximating polynomial for a differentiable function. MTAC 18 (1959), 185--193.
	10	PMES, E. Sur la Determination des polynomes d'approximation de degro donno. Communications de la soeioto mathematique de Kharkoff et de l'institut ds sciences mathematiques et m6chaniques de l'universit6 de Kharkoff, serie 4, t. X. Kharkoff 1934.
	11	Sur le ealcul effectif des polynomes d'approximation de Tchebycheff. Compt. Rend. Acad. Sci. Paris 199 (1934), 337-340.
	12	STIErEL, E. L. Numerical methods of Tchebycheff approximation. In On Numerical Approximation, R. E. Langer, Ed., 217-232, Madison 1959.
	13	STOER, J. -ber zwei Algorithmen zur Interpolation mit rationalen Funktionen. Num. Math. 3 (1961), 285-304.
	14	VEIDINGER, L. On the numerical determination of the best approximation in the Chebyshev sense. Num. Math. 2 (1960), 99-105.
	15	WERNER, H. Ein Satz iber diskrete Tschebyscheff-Approximation bei gebrochen linearen Funktionen. Num. Math. (1962), 154-157.
	16	WERNER, H. Tschebyscheff-Approximationen im Bereich der rationalen Funktionen bei Vorliegen einer guten Ausgangsnherung. Arch. Rat. Mech. Anal. 10 (1962), 205-219.
	17	WERNER, H. Die konstruktive Ermittlung der Tschbyscheff-Approximierenden im Bereich der rationalen Funktionen. Arch. Rat. Mech. Anal. 11 (1962), 368-384.
	18	WERNER, H. Rationale Tschebyscheff-Approximation, Eigenwerttheorie und Differenzenrechung. Arch. ra. Mech. Anol. 13 (1963), 330-347

CITED BY 2

	I. Gargantini, On the application of the process of equalization of maxima to obtain rational approximation to certain modified Bessel functions, Communications of the ACM, v.9 n.12, p.859-863, Dec. 1966
	M. Klein, Rational approximation via minimax linear programming regression, Proceedings of the 1968 23rd ACM national conference, p.79-84, August 27-29, 1968