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A Preconditioned Krylov Subspace Method for the Solution of Least Squares Problems in Inverse Scattering

✍ Scribed by Kees Vuik; Agur G.J. Sevink; Gérard C. Herman

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
384 KB
Volume
123
Category
Article
ISSN
0021-9991

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✦ Synopsis

In this paper we consider an underdetermined system of equations Lx ϭ b so m Ͻ n. However, the methods given

We present an iterative method of preconditioned Krylov type for the solution of large least squares problems. We prove that the in Section 3 can also be used for overdetermined systems.

method is robust and investigate its rate of convergence. For an It is easy to show that x is a solution of (1) if and only if important application, originating from seismic inverse scattering, we derive a suitable preconditioner using asymptotic theory. Numerical experiments are used to compare the method with other L*Lx ϭ L*b.

(2)

iterative methods. It appears that the preconditioned Krylov method can be much more efficient than CG applied to the normal equa-

The equations given in (2) are called the normal equations.

tions.

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