Applying Wavelet Transforms as a Solution for Convolution Type Equations

Authors: Lukianenko, Vladimir A.^Aff5

Contributors: Karapetyants, Alexey N., editor^Aff1, Kravchenko, Vladislav V., editor^Aff2, Liflyand, Elijah, editor^Aff3, Malonek, Helmuth R., editor^Aff4

Source: Operator Theory and Harmonic Analysis : OTHA 2020, Part I – New General Trends and Advances of the Theory. 357:369-391

Development of a numerical method for solving optimization problems approximation of the function given approximately and its derivatives based on the variational approach

Authors: Igor Naats, Victoria Igorevna Naats, Elena Yartseva

Source: Наука. Инновации. Технологии, Vol 0, Iss 4, Pp 7-20 (2022)

Subject Terms: аппроксимация функции, обобщенные полиномы, регуляризиру-ющие алгоритмы, сингулярные интегралы, вычислительный процесс, задачи прикладного анализа, function approximation, generalized polynomials, regularizing algorithms, singular integrals, computational process, applied analysis problems, Geography (General), G1-922

File Description: electronic resource

Relation: https://scienceit.elpub.ru/jour/article/view/167; https://doaj.org/toc/2308-4758

Access URL: https://doaj.org/article/acff0ba85eb74b2587c17814d8c8024f

METHODS OF APPROXIMATION OF FUNCTIONS BY GENERALIZED POLYNOMIALS IN NUMERICAL ANALYSIS PROBLEMS RELATED TO CALCULATIONS ON APPROXIMATE DATA

Authors: Igor Eduardovich Naats, Victoria Igorevna Naats, Elena Pavlovna Yartseva

Source: Наука. Инновации. Технологии, Vol 0, Iss 3, Pp 53-64 (2022)

Subject Terms: аппроксимация функции, обобщенные полиномы, регуляризирующие алгоритмы, сингулярные интегралы, вычислительный процесс, задачи прикладного анализа, function approximation, generalized polynomials, regularizing algorithms, singular integrals, computational process, applied analysis problems, Geography (General), G1-922

File Description: electronic resource

Relation: https://scienceit.elpub.ru/jour/article/view/181; https://doaj.org/toc/2308-4758

Access URL: https://doaj.org/article/f7707fb9030c4f0cbe301e70553bf2b7

Implicit Iterative Schemes Based on Augmented Linear Systems

Authors: Zhdanov, A. I.^{Aff1, IDS106456242202020X_cor1}

Source: Doklady Mathematics. 105(2):131-134

Extra-Optimal Methods for Solving Ill-Posed Problems: Survey of Theory and Examples

Authors: Leonov, A. S.^{Aff1, IDS0965542520060068_cor1}

Source: Computational Mathematics and Mathematical Physics. 60(6):960-986

Effective Algorithms for Computing Global and Local Posterior Error Estimates of Solutions to Linear Ill-Posed Problems

Authors: Leonov, A. S.^{Aff1, IDS1066369X20020048_cor1}

Source: Russian Mathematics. 64(2):26-34

Methods for Solving Ill-Posed Extremum Problems with Optimal and Extra-Optimal Properties

Authors: Leonov, A. S.^{Aff1, cor1}

Source: Mathematical Notes. 105(3-4):385-397

A New Algorithm for a Posteriori Error Estimation for Approximate Solutions of Linear Ill-Posed Problems

Authors: Leonov, A. S.^{Aff1, cor1}

Source: Computational Mathematics and Mathematical Physics. 59(2):193-200

Inverse problems in identification and modeling of thermal processes: Russian contributions

Authors: Alifanov, Oleg M.

Source: International Journal of Numerical Methods for Heat & Fluid Flow, 2017, Vol. 27, Issue 3, pp. 711-728.

Access URL: http://www.emeraldinsight.com/doi/10.1108/HFF-03-2016-0099

Application of Two-Parameter Stabilizing Functions in Solving a Convolution-Type Integral Equation by Regularization Method

Authors: Maslakov, M. L.^{Aff1, cor1}

Source: Computational Mathematics and Mathematical Physics. 58(4):529-536

Error Estimation in Ill-Posed Problems in Special Cases

Authors: Yagola, Anatoly G.^Aff2, Korolev, Yury M.^Aff2

Contributors: Beilina, Larisa, editor^Aff1

Source: Applied Inverse Problems : Select Contributions from the First Annual Workshop on Inverse Problems. 48:155-164

Regularizing algorithms with optimal and extra-optimal quality

Authors: Leonov, A. S.

Source: Numerical Analysis and Applications. October 2016 9(4):288-298

Regularizing algorithms for detecting discontinuities in ill-posed problems

Authors: T. V. Antonova, A. L. Ageev

Source: Computational Mathematics and Mathematical Physics. 48:1284-1292

Subject Terms: Linear operators and ill-posed problems, regularization, noisy function, 0102 computer and information sciences, 0101 mathematics, singularities, regularizing algorithms, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1134/S0965542508080034
https://ui.adsabs.harvard.edu/abs/2008CMMPh..48.1284A/abstract

Efficient algorithms for the regularization of dynamic inverse problems: I. Theory: Efficient algorithms for the regularization of dynamic inverse problems. I: Theory

Authors: Alfred K. Louis, Uwe Schmitt

Source: Inverse Problems. 18:645-658

Subject Terms: Hilbert spaces, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, dynamic inverse problem, measuring process, static inverse problem, Numerical solution to inverse problems in abstract spaces, Tikhonov Phillips method, 02 engineering and technology, regularizing algorithms, 01 natural sciences, linear operator equations, Numerical solutions to equations with linear operators, projection methods, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Equations and inequalities involving linear operators, with vector unknowns

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https://doi.org/10.1088/0266-5611/18/3/308
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http://iopscience.iop.org/article/10.1088/0266-5611/18/3/308/pdf

Efficient algorithms for the regularization of dynamic inverse problems: II. Applications: Efficient algorithms for the regularization of dynamic inverse problems. II: Applications

Authors: Schmitt, U., Louis, A., Wolters, C., Vauhkonen, M.

Source: Inverse Problems

Subject Terms: Biomedical imaging and signal processing, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, electrical impedance problem, Numerical solution to inverse problems in abstract spaces, regularizing algorithms, 01 natural sciences, dynamic inverse problems, density reconstruction, ill-posed problems, computational methods, 03 medical and health sciences, 0302 clinical medicine, Numerical solutions to equations with linear operators, statistical methods, Inverse problems (including inverse scattering) in optics and electromagnetic theory, computerized tomography, 0101 mathematics, Kalman filters, Equations and inequalities involving linear operators, with vector unknowns

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Access URL: https://pure.mpg.de/pubman/item/item_721912_5/component/file_721911/schmitt.pdf
https://zbmath.org/1787295
https://doi.org/10.1088/0266-5611/18/3/309
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http://ui.adsabs.harvard.edu/abs/2002InvPr..18..659S/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/18/3/309
https://core.ac.uk/display/45689193
http://hdl.handle.net/11858/00-001M-0000-0010-AF20-9
http://hdl.handle.net/11858/00-001M-0000-0010-AF21-7

On an algorithm for dynamic reconstruction in systems with delay in control

Authors: Blizorukova, M.

Source: IFIP Advances in Information and Communication Technology

Subject Terms: DYNAMIC RECONSTRUCTION, METHOD OF AUXILIARY MODELS, AUXILIARY MODELS, COMPUTATIONAL ERROR, IN-CONTROL, REGULARIZING ALGORITHMS, SYSTEMS WITH DELAYS, UNKNOWN INPUTS, VECTOR EQUATION, ALGORITHMS, OPTIMIZATION, NONLINEAR EQUATIONS

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Availability: http://elar.urfu.ru/handle/10995/75267
https://link.springer.com/content/pdf/10.1007%2F978-3-642-36062-6_23.pdf
http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=84874503461
https://doi.org/10.1007/978-3-642-36062-6_23

A posteriori accuracy estimations of solutions to ill-posed inverse problems and extra-optimal regularizing algorithms for their solution

Authors: Leonov, A. S.

Source: Numerical Analysis and Applications. January 2012 5(1):68-83

Regularizing properties of explicit approximating splines

Authors: A. I. Grebennikov

Source: Computational Mathematics and Modeling. 1:132-136

Subject Terms: Spline approximation, polynomial splines, 0101 mathematics, regularizing algorithms, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007%2FBF01129054

Regularizing algorithms for localization of breakpoints of noisy functions

Authors: Antonova, T. V.

Source: Proceedings of the Steklov Institute of Mathematics. September 2009 266(1):24-39

On the total-variation convergence of regularizing algorithms for ill-posed problems

Authors: Leonov, A. S.

Source: Computational Mathematics and Mathematical Physics. May 2007 47(5):732-747