Boolean Methods in Fourier Approximation

Accelerating Convergence of Univariate and Bivariate Fourier Approximations

“…Note that this representation is valid on the whole of Q unlike a corresponding result of [2]. In the case ft C'(Q) n 1 (r€ N) we have F,.!…”

“…Note that the representation (1.7) of f is valid on the whole of P unlike a corresponding result of [2].…”

“…Choosing h = Fr!, the Krylov -Lanczos method is an immediate consequence of the Taylor formula (1.7). Theorem 2.1 [2]: If fE C ( P) ( r , *!! 1), then we have the Krylov -Lanczos decompo -…”

“…The above one -dimensional approach to the Krylov -Lanczos method can be extented to the bivariate case by Gordons blending function method [2,4,6]. Let Q = Px P. For r N0 , let Cr.…”