SUPERLINEAR CONVERGENCE ESTIMATES FOR A CONJUGATE GRADIENT METHOD FOR THE BIHARMONIC EQUATION

Raymond H. CHAN; Thomas K. DELILLO; Mark A. HORN

doi:10.1137/S1064827596303570

Author(s)

Raymond H. CHAN
Thomas K. DELILLO
Mark A. HORN

Detail(s)

Original language	English
Pages (from-to)	139-147
Journal / Publication	SIAM Journal of Scientific Computing
Volume	19
Issue number	1
Publication status	Published - Jan 1998
Externally published	Yes

Link(s)

DOI	DOI https://doi.org/10.1137/S1064827596303570 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-2142788146&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(6ea66493-edee-4ccb-89ff-fe8e4b507f6f).html

Abstract

The method of Muskhelishvili for solving the biharmonic equation using conformal mapping is investigated. In [R. H. Chan, T. K. DeLillo, and M. A. Horn, SIAM J. Sci. Comput., 18 (1997), pp. 1571-1582] it was shown, using the Hankel structure, that the linear system in [N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, the Netherlands] is the discretization of the identity plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. Estimates are given here of the superlinear convergence in the cases when the boundary curve is analytic or in a Hölder class.

Research Area(s)

Biharmonic equation, Conjugate gradient method, Hankel matrices, Numerical conformal mapping

Citation Format(s)

[ RIS ] [ BibTeX ]

SUPERLINEAR CONVERGENCE ESTIMATES FOR A CONJUGATE GRADIENT METHOD FOR THE BIHARMONIC EQUATION. / CHAN, Raymond H.; DELILLO, Thomas K.; HORN, Mark A.
In: SIAM Journal of Scientific Computing, Vol. 19, No. 1, 01.1998, p. 139-147.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

CHAN, RH, DELILLO, TK & HORN, MA 1998, 'SUPERLINEAR CONVERGENCE ESTIMATES FOR A CONJUGATE GRADIENT METHOD FOR THE BIHARMONIC EQUATION', SIAM Journal of Scientific Computing, vol. 19, no. 1, pp. 139-147. https://doi.org/10.1137/S1064827596303570

CHAN, R. H., DELILLO, T. K., & HORN, M. A. (1998). SUPERLINEAR CONVERGENCE ESTIMATES FOR A CONJUGATE GRADIENT METHOD FOR THE BIHARMONIC EQUATION. SIAM Journal of Scientific Computing, 19(1), 139-147. https://doi.org/10.1137/S1064827596303570

CHAN RH, DELILLO TK, HORN MA. SUPERLINEAR CONVERGENCE ESTIMATES FOR A CONJUGATE GRADIENT METHOD FOR THE BIHARMONIC EQUATION. SIAM Journal of Scientific Computing. 1998 Jan;19(1):139-147. doi: 10.1137/S1064827596303570

CHAN, Raymond H. ; DELILLO, Thomas K. ; HORN, Mark A. / SUPERLINEAR CONVERGENCE ESTIMATES FOR A CONJUGATE GRADIENT METHOD FOR THE BIHARMONIC EQUATION. In: SIAM Journal of Scientific Computing. 1998 ; Vol. 19, No. 1. pp. 139-147.