About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Paper
On the Cholesky factorization of the Gram matrix of locally supported functions
Abstract
Cholesky factorization of bi-infinite and semi-infinite matrices is studied and in particular the following is proved. If a bi-infinite matrix A has a Cholesky factorization whose lower triangular factor L and its lower triangular inverse decay exponentially away from the diagonal, then the semi-infinite truncation of A has a lower triangular Cholesky factor whose elements approach those of L exponentially. This result is then applied to studying the asymptotic behavior of splines obtained by orthogonalizing a large finite set of B-splines, in particular identifying the limiting profile when the knots are equally spaced. © 1995 BIT Foundation.