Analysis on eigenvalues for preconditioning cubic spline collocation method of elliptic equations

Sang Dong Kim; Yong Hunlee

doi:10.1016/S0024-3795(00)00321-9

Analysis on eigenvalues for preconditioning cubic spline collocation method of elliptic equations

Sang Dong Kim^*
, Yong Hunlee

^*Corresponding author for this work

Department of Mathematics

Kyungpook National University

Research output: Contribution to journal › Journal article › peer-review

Abstract

In the work of solving a uniformly elliptic differential equations Au:=-Δu+a₁u_x+a₂u_y+a ₀u=f in the unit square with boundary conditions by the C¹-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix when a full finite element preconditioning is considered.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	327
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(00)00321-9
State	Published - 2001.04.15

Keywords

65F05
65F10
65N30
65N35

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Access to Document

10.1016/S0024-3795(00)00321-9

Cite this

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title = "Analysis on eigenvalues for preconditioning cubic spline collocation method of elliptic equations",

abstract = "In the work of solving a uniformly elliptic differential equations Au:=-Δu+a1ux+a2uy+a 0u=f in the unit square with boundary conditions by the C1-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix when a full finite element preconditioning is considered.",

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author = "\{Dong Kim\}, Sang and Yong Hunlee",

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T1 - Analysis on eigenvalues for preconditioning cubic spline collocation method of elliptic equations

AU - Dong Kim, Sang

AU - Hunlee, Yong

PY - 2001/4/15

Y1 - 2001/4/15

N2 - In the work of solving a uniformly elliptic differential equations Au:=-Δu+a1ux+a2uy+a 0u=f in the unit square with boundary conditions by the C1-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix when a full finite element preconditioning is considered.

AB - In the work of solving a uniformly elliptic differential equations Au:=-Δu+a1ux+a2uy+a 0u=f in the unit square with boundary conditions by the C1-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix when a full finite element preconditioning is considered.

KW - 65F05

KW - 65F10

KW - 65N30

KW - 65N35

UR - https://www.scopus.com/pages/publications/0035871470

U2 - 10.1016/S0024-3795(00)00321-9

DO - 10.1016/S0024-3795(00)00321-9

M3 - Journal article

AN - SCOPUS:0035871470

SN - 0024-3795

VL - 327

SP - 1

EP - 15

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

Analysis on eigenvalues for preconditioning cubic spline collocation method of elliptic equations

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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