The worst case complexity of the fredholm equation with periodic free term and noisy information^∗

The first author was supported by the Natural Science Foundation of China

Abstract

This paper deals with the complexity of the Fredholm equation L _u = fof the second kind with f[euro]H'(r) in a periodic setting. The problem elements are free term fand belong to the unit ball of H'(r). Available information about the problem element fis assumed to be corrupted by bounded noise. First, we give the order of the n-the optimal radius in the worst case setting. Then, we show that the Galerkin method using 2n+1 inner products of fhas minimal error. Finally, we give the estimate of ⌞complexity of the Fredholm integral equation of the second kind and the Galerkin method in the worst case setting.

Keywords:

• Worst case complexity
• Fredholm equation
• Galerkin method
• galerkin information
• noisy information

AMS Subject Classifications:

• 45B05
• 65R20

C.R. Categories:

• G.1.9
• F.2.2
• H.1.1

The first author was supported by the Natural Science Foundation of China

The first author was supported by the Natural Science Foundation of China

Notes

The first author was supported by the Natural Science Foundation of China