GMRES and integral operators

Conference · Sat Dec 31 04:00:00 EST 1994

DOI:https://doi.org/10.1137/0917015· OSTI ID:223842

Kelley, C T; Xue, Z Q ^[1]

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1. North Carolina State Univ., Raleigh, NC (United States)

Many discretizations of integral equations and compact fixed point problems are collectively compact and strongly convergent in spaces of continuous functions. These properties not only lead to stable and convergent approximations but also can be used in the construction of fast multilevel algorithms. Recently the GMRES algorithm has become a standard coarse mesh solver. The purpose of this paper is to show how the special properties of integral operators and their approximations are reflected in the performance of the GMRES iteration and how these properties can be used to strengthen the norm in which convergence takes place. The authors illustrate these ideas with composite Gauss rules for integral equations on the unit interval.

• Research Organization: Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• OSTI ID: 223842
• Report Number(s): CONF-9404305--Vol.1; ON: DE96005735
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
COMPUTER CALCULATIONS
CONVERGENCE
FINITE DIFFERENCE METHOD
G CODES
INTEGRAL EQUATIONS
ITERATIVE METHODS