When a Nyström-Broyden method is used to solve numerically Urysohn integral equations, the main problem is to evaluate the action of the integral operator at a low cost. Here we suitably approximate the relevant discrete integral operator of dimensionn by its m-degree truncated Chebyshev series expansion (with m≪n), reducing the complexity from the basic O(n^2) to O(m*n). A technique to evaluate cheaply such m is presented. Several linear and nonlinear examples are considered.
A fast Nystrom-Broyden solver by Chebyshev compression
SOMMARIVA, ALVISE
2005
Abstract
When a Nyström-Broyden method is used to solve numerically Urysohn integral equations, the main problem is to evaluate the action of the integral operator at a low cost. Here we suitably approximate the relevant discrete integral operator of dimensionn by its m-degree truncated Chebyshev series expansion (with m≪n), reducing the complexity from the basic O(n^2) to O(m*n). A technique to evaluate cheaply such m is presented. Several linear and nonlinear examples are considered.
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