000			03822cam a2200301 a 4500
008			100927s2011 gw a b 001 0 eng
020			_a9783110250640
020			_a3110250640
040			_aSDU
050	0	0	_aQA377 _bB166 I 2011
100	1		_aBakushinskiĭ, A. B. _9193027
245	1	0	_aIterative methods for ill-posed problems : _ban introduction / _cAnatoly B. Bakushinsky, Mikhail Yu. Kokurin, Alexandra Smirnova.
260			_aBerlin ; _aNew York : _bDe Gruyter, _c2011.
300			_a136 p. : _bill.
490	1		_aInverse and ill-posed problems series ; _v54
505	0	0	_tThe regularity condition. Newton's method -- _tPreliminary results -- _tLinearization procedure -- _tError analysis -- _tProblems -- _tThe Gauss -- Newton method -- _tMotivation -- _tConvergence rates -- _tProblems -- _tThe gradient method -- _tThe gradient method for regular problems -- _tIll-posed case -- _tProblems -- _tTikhonov's scheme -- _tThe Tikhonov functional -- _tProperties of a minimizing sequence -- _tOther types of convergence -- _tEquations with noisy data -- _tProblems -- _tTikhonov's scheme for linear equations -- _tThe main convergence result -- _tElements of spectral theory -- _tMinimizing sequences for linear equations
505	0	0	_tA priori agreement between the regularization parameter and the error for equations with perturbed right-hand sides -- _tThe discrepancy principle -- _tApproximation of a quasi-solution -- _tProblems -- _tThe gradient scheme for linear equations -- _tThe technique of spectral analysis -- _tA priori stopping rule -- _tA posteriori stopping rule -- _tProblems -- _tConvergence rates for the approximation methods in the case of linear irregular equations -- _tThe source-type condition (STC) -- _tSTC for the gradient method -- _tThe saturation phenomena -- _tApproximations in case of a perturbed STC -- _tAccuracy of the estimates -- _tProblems -- _tEquations with a convex discrepancy functional by Tikhonov's method -- _tSome difficulties associated with Tikhonov's method in case of a convex discrepancy functional
505	0	0	_tAn illustrative example -- _tProblems -- _tIterative regularization principle -- _tThe idea of iterative regularization -- _tThe iteratively regularized gradient method -- _tProblems -- _tThe iteratively regularized Gauss -- Newton method -- _tConvergence analysis -- _tFurther properties of IRGN iterations -- _tA unified approach to the construction of iterative methods for irregular equations -- _tThe reverse connection control -- _tProblems -- _tThe stable gradient method for irregular nonlinear equations -- _tSolving an auxiliary finite dimensional problem by the gradient descent method -- _tInvestigation of a difference inequality -- _tThe case of noisy data -- _tProblems -- _tRelative computational efficiency of iteratively regularized methods -- _tGeneralized Gauss -- Newton methods -- _tA more restrictive source condition
505	0	0	_tComparison to iteratively regularized gradient scheme -- _tProblems -- _tNumerical investigation of two-dimensional inverse gravimetry problem -- _tProblem formulation -- _tThe algorithm -- _tSimulations -- _tProblems -- _tIteratively regularized methods for inverse problem in optical tomography -- _tStatement of the problem -- _tSimple example -- _tForward simulation -- _tThe inverse problem -- _tNumerical results -- _tProblems -- _tFeigenbaum's universality equation -- _tThe universal constants -- _tIll-posedness -- _tNumerical algorithm for 2 ≤ z ≤ 12 -- _tRegularized method for z ≥ 13 -- _tProblems -- _tConclusion.
505	0	0	_tHKBU library
518			_aYT2025 M10
650		0	_aDifferential equations, Partial _xImproperly posed problems. _9193028
650		0	_aIterative methods (Mathematics) _9193029
700	1		_aKokurin, M. I︠U︡. _9193030
700	1		_aSmirnova, A. B. _9193031
900			_a= C.1 SDU
942			_cGBE _2lcc
999			_c103936 _d103936