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Autor: Bialecki, Bernard (Comienzo)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Aitbayev, Rakhim ; Bialecki, Bernard
Título: A Preconditioned Conjugate Gradient Method for Nonselfadjoint or Indefinite Orthogonal Spline Collocation Problems
Páginas/Colación: pp. 589 - 604
Url: Ir a http://epubs.siam.org/sam-bin/dbq/article/39139http://epubs.siam.org/sam-bin/dbq/article/39139
Siam Journal on Numerical Analysis Vol. 41, no. 2 April-May 2004
Información de existenciaInformación de existencia

Palabras Claves: Palabras: CONJUGATE GRADIENT METHOD CONJUGATE GRADIENT METHOD, Palabras: MATRIX DECOMPOSITION ALGORITHM MATRIX DECOMPOSITION ALGORITHM, Palabras: NONSELFADJOINT OR INDEFINITE ELLIPTIC BOUNDARY VALUE PROBLEM NONSELFADJOINT OR INDEFINITE ELLIPTIC BOUNDARY VALUE PROBLEM, Palabras: ORTHOGONAL SPLINE COLLOCATION ORTHOGONAL SPLINE COLLOCATION, Palabras: PRECONDITIONER PRECONDITIONER

Resumen
We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form $Lu=\sum a_{ij}(x)u_{x_ix_j}+\sum b_i(x) u_{x_i}+c(x)u$. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a separable operator, and prove that the resulting algorithm has a convergence rate independent of the partition step size. We solve a problem with the preconditioner using an efficient direct matrix decomposition algorithm. On a uniform N × N partition, the cost of the algorithm for computing the collocation solution within a tolerance $\epsilon$ is O$(N^{2}\ln N |\ln \epsilon|)$.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Abushama , Abeer Ali ; Bialecki, Bernard
Título: Modified Nodal Cubic Spline Collocation For Poisson's Equation
Páginas/Colación: pp. 397-418
Fecha: Vol. 46, No. 1
Url: Ir a http://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJNAAM000046000001000397000001&idtype=cvips&gifs=Yeshttp://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJNAAM000046000001000397000001&idtype=cvips&gifs=Yes
Siam Journal on Numerical Analysis Vol. 44, no. 1 February.2007
Información de existenciaInformación de existencia

Resumen
RESUMEN

RESUMEN

 

We present a new modified nodal cubic spline collocation scheme for solving the Dirichlet problem for Poisson’s  equation on the unit square. We prove existence and uniqueness of a solution of the scheme and show how the solution can be computed on an (N + 1) × (N + 1) uniform partition of the square with cost O(N2logN) using a direct fast Fourier transform method. Using two comparison functions, we derive an optimal fourth order error bound in the continuous maximum norm. We compare our scheme with other modified nodal cubic spline collocation schemes; in particular, the one proposed by Houstis, Vavalis, and Rice in [SIAM J. Numer. Anal., 25 (1988), pp. 54–74]. We believe that our paper gives the first correct convergence analysis of a modified nodal cubic spline collocation for solving partial differential equations.

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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