On the Cholesky Factorization of the Gram Matrix of Multivariate Functions

Authors:
Tim N. T. Goodman;Charles A. Micchelli;Giuseppe Rodriguez;Sebastiano Seatzu
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2000

Citing 0
Cited 3

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Abstract

We study the Cholesky factorization of certain bi-infinite matrices and related finite matrices. These results are applied to show that if the uniform translates of a suitably decaying multivariate function are orthonormalized by the Gram--Schmidt process over certain increasing finite sets, then the resulting functions converge to translates of a fixed function which is obtained by a global orthonormalization procedure. This convergence is also illustrated numerically.