PERFECT SPLINES WITH BOUNDARY-CONDITIONS OF LEAST NORM

[摘要] Let A = (a(ij))i = 1, j = 0 l, r - 1 and B = (b(ij))i = 1, j = 0 m, r - 1 be matrices of ranks l and m. respectively. Suppose that A = (( - 1)j a(ij)) is-an-element-of SC(j) (sign consistent of order l) and B is-an-element-of SC(m). Denote by P(r,N)(A, B; nu1, ..., nu(n)) the set of perfect splines with N knots which have n distinct zeros in (0, 1) with multiplicities nu(1, ..., nu(n), respectively. and satisfy AP(0)BAR = 0, BP(1)BAR = 0, where P(a)BAR = (p(a), ..., P(r-1)(a))T. We show that there is a unique P* is-an-element-of P(r,N)(A, B; nu1, ..., nu(n)) of least uniform norm and that P* is characterized by the equioscillatory property. This is closely related to the optimal recovery of smooth functions satisfying boundary conditions by using the Hermite data. (C) 1994 Academic Press, Inc.

[发布日期] 1994-05-01