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Full-Text Articles in Physical Sciences and Mathematics
Theoretical And Numerical Study Of Tikhonov's Regularization And Morozov's Discrepancy Principle, Marygeorge L. Whitney
Theoretical And Numerical Study Of Tikhonov's Regularization And Morozov's Discrepancy Principle, Marygeorge L. Whitney
Mathematics Theses
A concept of a well-posed problem was initially introduced by J. Hadamard in 1923, who expressed the idea that every mathematical model should have a unique solution, stable with respect to noise in the input data. If at least one of those properties is violated, the problem is ill-posed (and unstable). There are numerous examples of ill- posed problems in computational mathematics and applications. Classical numerical algorithms, when used for an ill-posed model, turn out to be divergent. Hence one has to develop special regularization techniques, which take advantage of an a priori information (normally available), in order to solve …