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Journal Articles SIAM Journal on Mathematical Analysis Year : 2014

The exact condition number of the truncated singular value solution of a linear ill-posed problem

Abstract

The main result of this paper is the formulation of an explicit expression for the condition number of the truncated least squares solution of $Ax=b$. This expression is given in terms of the singular values of $A$ and the Fourier coefficients of $b$. The result is derived using the notion of the Fréchet derivative together with the product norm on the data $[A,b]$ and the 2-norm on the solution. Numerical experiments are given to confirm our results by comparing them to those obtained by means of a finite difference approach.
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Dates and versions

hal-02147972 , version 1 (05-06-2019)

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El Houcine Bergou, Serge Gratton, Jean Tshimanga Ilunga. The exact condition number of the truncated singular value solution of a linear ill-posed problem. SIAM Journal on Mathematical Analysis, 2014, 35 (3), pp.1073-1085. ⟨10.1137/120869286⟩. ⟨hal-02147972⟩
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