Solution of convolution-type integral equations of the first kind in the multidimensional case

Савелова, Т.И.; Тихомиров, В.В.

doi:10.1016/0041-5553(73)90097-9

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“…At the solution of integral equations of the first kind of convolution type with kernels of the most general types, with the aid of summation Fourier integrals by factors with parameter a, under certain properties of the noise (error) in the right-hand side of the equation, one has obtained the systematic (depending on ~) and the random (depending on the noise) error components of the regularized solution, and, by setting them equal to each other, one selects an "almost optimal" value of a [30,34,307,349]; at the absence of information on the magni-tude of the maximum of the derivative of the exact solution the method can be improved [40] on the basis of the minimization of the sensitivity function M(llSxJSln all); here and in the sequel, M is the mathematical expectation symbol.…”

Section: Methodsmentioning

confidence: 99%

Theory and the methods of solution of ill-posed problems

Liskovets¹

1986

J Math Sci

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One gives a survey of the fundamental directions and results up to 1981, inclusively, regarding the topic mentioned in the title.In the last 25 years, under the direct influence of imperative practical needs of various areas of science and engineering, a new branch of mathematics, the theory and methods of solution of ill-posed problems, has been developed in a very intensive manner. Presently one totals close to 3000 publications in this topic. Many interesting and important results obtained up to 1972 are reflected in V. A. Morozov's extensive survey [264]. Since then, the theory of ill-posed problems has been significantly enriched and has become an independent discipline; this is attested by the apparition of numerous monographs devoted entirely or in a large part to this circle of questions ( ) and also by the inclusion of corresponding chapters in university textbooks and manuals [18, 31, 59, 79, 83, 176, 177, 187, 191, 201, 240, etc

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Section: Methodsmentioning

confidence: 99%

Theory and the methods of solution of ill-posed problems

Liskovets¹

1986

J Math Sci

View full text Add to dashboard Cite

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Solution of convolution-type integral equations of the first kind in the multidimensional case

Cited by 1 publication

References 2 publications

Theory and the methods of solution of ill-posed problems

Theory and the methods of solution of ill-posed problems

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