A method to compute recurrence relation coefficients for bivariate orthogonal polynomials by unitary matrix transformations.

Autor:	Barel, Marc Van, Chesnokov, Andrey
Předmět:	ORTHOGONAL polynomials POINT mappings (Mathematics) UNITARY transformations EIGENVALUES STATISTICAL correlation
Zdroj:	Numerical Algorithms; Nov2010, Vol. 55 Issue 2/3, p383-402, 20p, 2 Charts, 5 Graphs
Abstrakt:	We present an algorithm computing recurrence relation coefficients for bivariate polynomials, orthonormal with respect to a discrete inner product. These polynomials make it possible to give the solution of a discrete least squares approximation problem. To compute these polynomials, we pose the inverse eigenvalue problem and solve it efficiently and in a stable way, using a sequence of Givens rotations. We also show how to generalize the algorithm for the case of polynomials in more variables. Several numerical experiments show the validity of the approach. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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