1997, Mathematics in science and engineering, ISBN 9780120567454, Volume 194, 319

Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and...

Differential equations, Partial | Improperly posed problems | Mathematics

Differential equations, Partial | Improperly posed problems | Mathematics

eBook

1998, 1st ed., Applied mathematics and mathematical computation, ISBN 9780412786600, Volume 14., 2 v. (387 p.)

Book

Journal of Inverse and Ill-posed Problems, ISSN 0928-0219, 06/2019, Volume 27, Issue 3, pp. 453 - 456

Journal Article

Numerische Mathematik, ISSN 0029-599X, 8/2019, Volume 142, Issue 4, pp. 789 - 832

This work is concerned with the iterative regularization of a non-smooth nonlinear ill-posed problem where the forward mapping is merely directionally but not...

90C31 | Mathematical Methods in Physics | 49K20 | 49K40 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | MATHEMATICS, APPLIED | CONVERGENCE | PARAMETER-IDENTIFICATION | REGULARIZATION

90C31 | Mathematical Methods in Physics | 49K20 | 49K40 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | MATHEMATICS, APPLIED | CONVERGENCE | PARAMETER-IDENTIFICATION | REGULARIZATION

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 12/2016, Volume 1789, Issue 1

This paper deals with Protter problems for Keldysh type equations in ℝ4. Originally such type problems are formulated by M. Protter for equations of Tricomi...

Problems | Mathematical analysis | Ill-posed problems (mathematics)

Problems | Mathematical analysis | Ill-posed problems (mathematics)

Journal Article

Journal of Mathematical Sciences, ISSN 1072-3374, 3/2019, Volume 237, Issue 6, pp. 804 - 809

The paper discusses the de-noising method in a model with an additive Gaussian noise, based on the wavelet-vaguelette decomposition and thresholding of the...

Mathematics, general | Mathematics

Mathematics, general | Mathematics

Journal Article

Applied Physics Letters, ISSN 0003-6951, 09/2019, Volume 115, Issue 12

Random two-frame phase-shifting interferometry (PSI) is an advanced technique to retrieve the phase information from as few as two interferograms with unknown...

Computer simulation | Phase shifters | Information retrieval | Ill-posed problems (mathematics) | Coefficient of variation | Optimization | Interferometry

Computer simulation | Phase shifters | Information retrieval | Ill-posed problems (mathematics) | Coefficient of variation | Optimization | Interferometry

Journal Article

Doklady Mathematics, ISSN 1064-5624, 11/2018, Volume 98, Issue 3, pp. 603 - 606

For optimal control problems, a new approach based on the search for an extremum of a special functional is proposed. The differential problem is reformulated...

Mathematics, general | Mathematics | MATHEMATICS

Mathematics, general | Mathematics | MATHEMATICS

Journal Article

9.
Full Text
ON FRACTIONAL ASYMPTOTICAL REGULARIZATION OF LINEAR ILL-POSED PROBLEMS IN HILBERT SPACES

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, ISSN 1311-0454, 06/2019, Volume 22, Issue 3, pp. 699 - 721

In this paper, we study a fractional-order variant of the asymptotical regularization method, called Fractional Asymptotical Regularization (FAR), for solving...

MATHEMATICS | acceleration | MATHEMATICS, APPLIED | linear ill-posed operator equation | fractional derivatives | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | stopping rules | source conditions | convergence rates | asymptotical regularization | Asymptotic properties | Regularization methods | Hilbert space | Ill-posed problems (mathematics) | Acceleration | Iterative methods | Regularization | Smoothness

MATHEMATICS | acceleration | MATHEMATICS, APPLIED | linear ill-posed operator equation | fractional derivatives | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | stopping rules | source conditions | convergence rates | asymptotical regularization | Asymptotic properties | Regularization methods | Hilbert space | Ill-posed problems (mathematics) | Acceleration | Iterative methods | Regularization | Smoothness

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 10/2016, Volume 1776, Issue 1

We study a discrete bilevel problem, called as well as leader-follower problem, with multiple objectives at the lower level. It is assumed that constraints at...

Mixed integer | Series (mathematics) | Ill-posed problems (mathematics) | Heuristic

Mixed integer | Series (mathematics) | Ill-posed problems (mathematics) | Heuristic

Journal Article

11.
Full Text
Indirect Boundary Integral Equation Method for the Cauchy Problem of the Laplace Equation

Journal of Scientific Computing, ISSN 0885-7474, 5/2017, Volume 71, Issue 2, pp. 469 - 498

In this paper, we examine the Cauchy problem of the Laplace equation. Motivated by the incompleteness of the single-layer potential function method, we...

65R32 | Computational Mathematics and Numerical Analysis | Algorithms | 31A25 | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | 65N21 | Boundary element method | Morozov discrepancy principle | Cauchy problem | MATHEMATICS, APPLIED | LINEAR ELASTICITY | ALGORITHM | NUMERICAL EXPERIMENTS | POTENTIAL PROBLEMS | FORMULATION | ELLIPTIC-OPERATORS | ELEMENT SOLUTION | KERNEL | REGULARIZATION | DEGENERATE SCALE | Signal processing | Analysis | Methods

65R32 | Computational Mathematics and Numerical Analysis | Algorithms | 31A25 | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | 65N21 | Boundary element method | Morozov discrepancy principle | Cauchy problem | MATHEMATICS, APPLIED | LINEAR ELASTICITY | ALGORITHM | NUMERICAL EXPERIMENTS | POTENTIAL PROBLEMS | FORMULATION | ELLIPTIC-OPERATORS | ELEMENT SOLUTION | KERNEL | REGULARIZATION | DEGENERATE SCALE | Signal processing | Analysis | Methods

Journal Article

Structural and Multidisciplinary Optimization, ISSN 1615-147X, 3/2017, Volume 55, Issue 3, pp. 1017 - 1028

Material distribution topology optimization problems are generally ill-posed if no restriction or regularization method is used. To deal with these issues,...

Engineering | Computational Mathematics and Numerical Analysis | Nonlinear filters | Topology optimization | Engineering Design | Theoretical and Applied Mechanics | Regularization | Existence of solutions | Large-scale problems | PROJECTION | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | LENGTH SCALE | Regularization methods | Ill-posed problems (mathematics) | Naturvetenskap | Computational Mathematics | Mathematics | Natural Sciences | Beräkningsmatematik | Matematik

Engineering | Computational Mathematics and Numerical Analysis | Nonlinear filters | Topology optimization | Engineering Design | Theoretical and Applied Mechanics | Regularization | Existence of solutions | Large-scale problems | PROJECTION | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | LENGTH SCALE | Regularization methods | Ill-posed problems (mathematics) | Naturvetenskap | Computational Mathematics | Mathematics | Natural Sciences | Beräkningsmatematik | Matematik

Journal Article

BIT Numerical Mathematics, ISSN 0006-3835, 05/2018, Volume 58, Issue 3, pp. 1 - 2

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s10543-018-0708-y The...

Image processing | Methods

Image processing | Methods

Journal Article

Journal of the Physical Society of Japan, ISSN 0031-9015, 08/2018, Volume 87, Issue 8, p. 1

In natural sciences and engineering, observed data are often measured as a wrapped phase. Phase unwrapping is the problem of restoring such discontinuous...

Studies | Engineering | Inverse problems | Signal processing | Markov chains | Models | Ill-posed problems (mathematics) | Fields (mathematics) | Experiments | Bayesian analysis

Studies | Engineering | Inverse problems | Signal processing | Markov chains | Models | Ill-posed problems (mathematics) | Fields (mathematics) | Experiments | Bayesian analysis

Journal Article

Mathematical Problems in Engineering, ISSN 1024-123X, 2018, Volume 2018, pp. 1 - 16

This paper presents a novel inverse technique to provide a stable optimal solution for the ill-posed dynamic force identification problems. Due to...

OPERATOR-DEPENDENT SEMINORMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | INVERSE PROBLEM | APPROXIMATION | ILL-POSED PROBLEMS | TEXTURED IMAGES | CONVERGENCE | SYSTEMS | PRINCIPLE | CONSTRAINED OPTIMIZATION | ORDER REGULARIZATION | Fault diagnosis | Mathematical problems | Engineering | Algorithms | Inverse problems | Robustness (mathematics) | Applied mathematics | Regularization methods | Computational mathematics | Ill-posed problems (mathematics) | Parameter identification | Regularization

OPERATOR-DEPENDENT SEMINORMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | INVERSE PROBLEM | APPROXIMATION | ILL-POSED PROBLEMS | TEXTURED IMAGES | CONVERGENCE | SYSTEMS | PRINCIPLE | CONSTRAINED OPTIMIZATION | ORDER REGULARIZATION | Fault diagnosis | Mathematical problems | Engineering | Algorithms | Inverse problems | Robustness (mathematics) | Applied mathematics | Regularization methods | Computational mathematics | Ill-posed problems (mathematics) | Parameter identification | Regularization

Journal Article

Mechanical Systems and Signal Processing, ISSN 0888-3270, 05/2018, Volume 104, p. 1

Dynamic forces reconstruction from vibration data is an ill-posed inverse problem. A standard approach to stabilize the reconstruction consists in using some...

Studies | Reconstruction | Validity | Vibration | Inverse problems | Standard deviation | Excitation | Ill-posed problems (mathematics) | Regularization

Studies | Reconstruction | Validity | Vibration | Inverse problems | Standard deviation | Excitation | Ill-posed problems (mathematics) | Regularization

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2019, Volume 183, Issue 2, pp. 688 - 704

In this paper, we consider an inverse reaction–diffusion–convection problem in which one of the boundary conditions is unknown. A sixth-kind Chebyshev...

35R30 | Mollification | Mathematics | Theory of Computation | 35K15 | 41A50 | Reaction–diffusion–convection equation | Optimization | Inverse problem | Calculus of Variations and Optimal Control; Optimization | 65M70 | Operations Research/Decision Theory | Error estimate | Applications of Mathematics | Engineering, general | Collocation method | Sixth-kind Chebyshev polynomials | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Reaction-diffusion-convection equation | Algorithms | Inverse problems | Chebyshev approximation | Collocation methods | Boundary conditions | Regularization methods | Ill-posed problems (mathematics) | Regularization | Convection

35R30 | Mollification | Mathematics | Theory of Computation | 35K15 | 41A50 | Reaction–diffusion–convection equation | Optimization | Inverse problem | Calculus of Variations and Optimal Control; Optimization | 65M70 | Operations Research/Decision Theory | Error estimate | Applications of Mathematics | Engineering, general | Collocation method | Sixth-kind Chebyshev polynomials | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Reaction-diffusion-convection equation | Algorithms | Inverse problems | Chebyshev approximation | Collocation methods | Boundary conditions | Regularization methods | Ill-posed problems (mathematics) | Regularization | Convection

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 14

The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p=45 $p=45$ requiring 10...

Perturbation error analysis | Moore–Penrose inverse | Image restoration problem | Analysis | 65F30 | 65F20 | Mathematics, general | Mathematics | Applications of Mathematics | Linear least squares problems | Matrix algorithms | MATHEMATICS | MATHEMATICS, APPLIED | INVERSES | Moore-Penrose inverse | FAMILY | Predictor-corrector methods | Algorithms | Error analysis | Perturbation methods | Least squares | Aircraft industry | Image restoration | Ill-posed problems (mathematics) | Iterative methods | Convergence

Perturbation error analysis | Moore–Penrose inverse | Image restoration problem | Analysis | 65F30 | 65F20 | Mathematics, general | Mathematics | Applications of Mathematics | Linear least squares problems | Matrix algorithms | MATHEMATICS | MATHEMATICS, APPLIED | INVERSES | Moore-Penrose inverse | FAMILY | Predictor-corrector methods | Algorithms | Error analysis | Perturbation methods | Least squares | Aircraft industry | Image restoration | Ill-posed problems (mathematics) | Iterative methods | Convergence

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 01/2019, Volume 77, Issue 1, pp. 15 - 33

We study for the first time the backward problem for nonlocal nonlinear boundary value problem of Kirchhoff’s model of parabolic type. First, we show that the...

Ill-posed problem | Backward problem | Quasi-reversibility method | regularization | Boundary value problems | Ill-posed problems (mathematics)

Ill-posed problem | Backward problem | Quasi-reversibility method | regularization | Boundary value problems | Ill-posed problems (mathematics)

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 4/2019, Volume 45, Issue 2, pp. 735 - 755

The ill-posed continuation problem for the one-dimensional parabolic equation with the data given on the part of the boundary is investigated. We prove the...

Finite-difference scheme inversion | Visualization | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Numerical methods | Continuation problem | Mathematics | Computational Science and Engineering | 35K35 | Parabolic equation | Mathematical Modeling and Industrial Mathematics | Gradient method | 49N45 | Singular value decomposition | 65M32 | MATHEMATICS, APPLIED | Boundary value problems | Numerical analysis | Research | Differential equations, Partial | Mathematical research | Equations, Quadratic

Finite-difference scheme inversion | Visualization | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Numerical methods | Continuation problem | Mathematics | Computational Science and Engineering | 35K35 | Parabolic equation | Mathematical Modeling and Industrial Mathematics | Gradient method | 49N45 | Singular value decomposition | 65M32 | MATHEMATICS, APPLIED | Boundary value problems | Numerical analysis | Research | Differential equations, Partial | Mathematical research | Equations, Quadratic

Journal Article

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