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    Novel Iterative Algorithms Based on Regularization Total Least Squares for Solving the Numerical Solution of Discrete Fredholm Integral Equation

    Zichun Yang1,2,3, Lei Zhang1,4, Yueyun Cao1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 101-130, 2014, DOI:10.3970/cmes.2014.097.101

    Abstract Discretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov… More >

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