Integral equations of the first kind, inverse problems and regularization: a crash course
By Charles W. Groetsch. 2007
93 citations recorded by the source corpus.
This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the first kind and related background material on inverse problems. We begin with an historical introduction to the field of integral equations of the first kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of the first kind, paying particular attention to E. Schmidt's singular function analysis, Picard's existence criterion, and the Moore-Penrose theory of generalized inverses is outlined. The fundamentals of the theory of Tikhonov regularization are then treated and a collection of exercises and a bibliography are provided.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/d08dd6acb7f6048efe5de4f8bb301e473b9354c6
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In Computational Theory and Mathematics
In Mathematical Physics
In Mechanics of Materials
Citations in the corpus
- The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory (2011, methodology): “For an introductory account on integral equations, rich in examples and historical remarks, see [25].”