Least-squares fitting using orthogonal multinomials

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

• 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.

INDEX TERMS

Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Least squares methods

General Terms:
Algorithms

Keywords:
data fitting, multinomials, orthogonal, regression