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On numerical solution of arbitrary symmetric linear systems by approximate orthogonalization

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  • Popa, C.

Abstract

A very important class of inverse problems are those modelled by integral equations of the first kind. These equations are usually ill-conditioned, such that any discretization technique will produce an ill-conditioned system, in classical or least-squares formulation. For such kind of symmetric problems, we propose in this paper a stable iterative solver based on an approximate orthogonalization algorithm introduced by Z. Kovarik. We prove convergence of our algorithm for general symmetric least-squares problems and present some numerical experiments ilustrating its good behaviour on problems concerned with the determination of charge distribution generating a given electric field and gravity surveying, both modelled by first kind integral equations.

Suggested Citation

  • Popa, C., 2008. "On numerical solution of arbitrary symmetric linear systems by approximate orthogonalization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1033-1038.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:4:p:1033-1038
    DOI: 10.1016/j.matcom.2008.02.010
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