Least-squares fitting using orthogonal multinomials

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Least-squares fitting using orthogonal multinomials

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 11 , Issue 3 (September 1985) table of contents

Pages: 201 - 217

Year of Publication: 1985

ISSN:0098-3500

Authors

Richard H. Bartels	Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G2
John J. Jezioranski	Ontario Cancer Institute, 500 Sherbourne, St., Toronto, Ontario, Canada M4X 1K9

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 5, Downloads (12 Months): 38, Citation Count: 2

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ABSTRACT

Forsythe has given a method for generating basis polynomials in a single variable that are orthogonal with respect to a given inner product. Weisfeld later demonstrated that Forsythe's approach could be extended to polynomials in an arbitrary number of variables. In this paper we sharpen Weisfeld's results and present a method for computing weighted, multinomial, least-squares approximations to given data.

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	CADWELL, J. H., AND WILLIAMS, D.E. Some orthogonal methods of curve and surface fitting. Comput. J. 4 (1961), 260-261.
	2	DRAPER, N. R., AND SMITH, H. Applied Regression Analysis. Wiley, New York, 1980.
	3	FORSYTHE, G.E. Generation and use of orthogonal polynomials for data-fitting with a digital computer. J. SIAM 5 (1957), 74-87.
	4	IMSL. RLEAP. The International Mathematical and Statistical Libraries, Houston, Texas, 1984.
	5	RYDER, B.G. The PFORT verifier. Softw. Pract. Exper. 4 (1974), 359-377.
	6	WEISFELD, M. Orthogonal polynomials in several variables. Numer. Math. 1 (1959), 38-40.

CITED BY 2

	Richard H. Bartels , John J. Jezioranski, ALGORITHM 634: CONSTR and EVAL: routines for fitting multinomials in a least-squares sense, ACM Transactions on Mathematical Software (TOMS), v.11 n.3, p.218-228, Sept. 1985
	P. J. Besl , R. C. Jain, Segmentation through Variable-Order Surface Fitting, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.10 n.2, p.167-192, March 1988