On the Cholesky Factorization of the Gram Matrix of Multivariate Functions
Tim N.T. Goodman, Charles A. Micchelli, Giuseppe Rodriguez, S. Seatzu · SIAM Journal on Matrix Analysis and Applications · 2000
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.