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    A Globally Optimal Iterative Algorithm to Solve an Ill-Posed Linear System

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 383-404, 2012, DOI:10.3970/cmes.2012.084.383

    Abstract An iterative algorithm based on the critical descent vector is proposed to solve an ill-posed linear system: Bx = b. We define a future cone in the Minkowski space as an invariant manifold, wherein the discrete dynamics evolves. A critical value αc in the critical descent vector u = αcr + BTr is derived, which renders the largest convergence rate as to be the globally optimal iterative algorithm (GOIA) among all the numerically iterative algorithms with the descent vector having the form u = αr + BTr to solve the ill-posed linear problems. Some numerical examples are used to reveal… More >

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