Theory and Methods Related to the Singular-Function Expansion and Landweber's Iteration for Integral Equations of the First Kind
作者： Otto Neall Strand
DOI: 10.1137/0711066
关键词: Mathematics 、 Pure mathematics 、 Convergence (routing) 、 Function (mathematics) 、 Integral equation 、 Fredholm integral equation 、 Matrix (mathematics) 、 Linear map 、 Discrete mathematics 、 Uniqueness theorem for Poisson's equation 、 Singular function
摘要: For the Fredholm integral equation of first kind, written notationally as $Kf = g$, $g \in L_2 [0,1]$, we study behavior iteration \[ \hat f_k f_{k - 1} + DK^ * (g K\hat ),\quad k 1,2, \cdots ,\] both with respect to its convergence properties and response singular functions K. Here $K^ $ is adjoint K, $\hat f_0 a suitable starting function D fixed linear operator be chosen. The general theory interpreted extended for iteration, quantitative method choosing shape K derived. Several specific matrix integral-equation examples are presented.
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