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    Double Optimal Regularization Algorithms for Solving Ill-Posed Linear Problems under Large Noise

    Chein-Shan Liu1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.1, pp. 1-39, 2015, DOI:10.3970/cmes.2015.104.001

    Abstract A double optimal solution of an n-dimensional system of linear equations Ax = b has been derived in an affine m « n. We further develop a double optimal iterative algorithm (DOIA), with the descent direction z being solved from the residual equation Az = r0 by using its double optimal solution, to solve ill-posed linear problem under large noise. The DOIA is proven to be absolutely convergent step-by-step with the square residual error ||r||2 = ||b - Ax||2 being reduced by a positive quantity ||Azk||2 at each iteration step, which is found to be better than those algorithms based More >

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