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Convergence of multipower defect-correction for spectral computations of integral operators. (English) Zbl 1293.65176

Summary: We propose the multipower defect-correction method, a generalization of the double iteration, to compute a cluster of eigenvalues and the associated invariant subspace from discretized integral operators. It consists of an inner/outer iteration where, inside a defect-correction iteration, \(p\) power iteration steps are performed. The approximate inverse used in the defect correction is built with an approximation to the reduced resolvent operator of a coarse discretization of the integral operator. The proposed method computes eigenpairs approximations by refining initial approximations obtained from a coarser dimensional problem. It is therefore meant for large dimensional problems. Furthermore, the kernel of the integral operator may be weakly singular. We provide a proof for the convergence of this multipower defect-correction method. A numerical example illustrating the theory and the behavior of the method is also presented.

MSC:

65R20 Numerical methods for integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
45P05 Integral operators
45C05 Eigenvalue problems for integral equations
47G10 Integral operators
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References:

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