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On the Cholesky factorization of the Gram matrix of locally supported functions (1995)

Goodman, T. N. T. ; Micchelli, C. A. ; Rodriguez, G. ; [et al.]

Springer

BIT 35 (1995), S. 233-257

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ISSN: 1572-9125

Keywords: Cholesky factorization ; Gram matrix ; orthogonal splines ; B-splines

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Cholesky factorization of bi-infinite and semi-infinite matrices is studied and in particular the following is proved. If a bi-infinite matrixA has a Cholesky factorization whose lower triangular factorL and its lower triangular inverse decay exponentially away from the diagonal, then the semi-infinite truncation ofA has a lower triangular Cholesky factor whose elements approach those ofL 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01737164

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