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International journal of mathematics, ISSN 1793-6519, 2018, Volume 29, Issue 12, p. 1850084
We introduce an unknotting-type number of knot projections that gives an upper bound of the crosscap number of knots... 
Crosscap number (non-orientable genus) | spanning surfaces | knot projection | alternating knot | MATHEMATICS
Journal Article
Foundations of computational mathematics, ISSN 1615-3383, 2008, Volume 9, Issue 4, pp. 485 - 513
... (convexity or smoothness, for example), we prove that von Neumann's method of "alternating projections" converges locally to a point in the intersection, at a linear rate associated with a modulus of regularity... 
Alternating projections | Extremal principle | Variational analysis | Linear convergence | Averaged projections | Distance to ill-posedness | Nonconvexity | Metric regularity | Prox-regularity | MATRIX | MATHEMATICS, APPLIED | VARIANTS | DIFFERENTIABILITY | COMPLEXITY THEORY | PROXIMAL POINT ALGORITHM | MATHEMATICS | REGULARITY | COMPUTER SCIENCE, THEORY & METHODS | Mathematical problems | Variance analysis | Algorithms | Mathematics | Optimization and Control
Journal Article
Applied and computational harmonic analysis, ISSN 1063-5203, 2016, Volume 41, Issue 3, pp. 815 - 851
We demonstrate necessary and sufficient conditions of the local convergence of the alternating projection algorithm to a unique solution up to a global phase factor... 
Alternating projection | Graph connection Laplacian | Phase retrieval | Phase synchronization | Ptychography | MATHEMATICS, APPLIED | RECONSTRUCTION | RESOLUTION | X-RAY-DIFFRACTION | ELECTRON-DIFFRACTION | COMPUTED-TOMOGRAPHY | RETRIEVAL | Algorithms
Journal Article
Journal Article
Constructive Approximation, ISSN 0176-4276, 12/2013, Volume 38, Issue 3, pp. 489 - 525
...}$ . Under appropriate conditions, we prove not only that the sequence of alternating projections converges, but that the limit point is fairly close to B opt , in a manner relative to the distance ∥B 0−B opt ∥, thereby significantly improving earlier results in the field. 
Alternating projections | Manifolds | 53B25 | Low-rank approximation | Numerical Analysis | Analysis | 41A65 | Mathematics | 49Q99 | Non-convexity | Convergence | MATHEMATICS | MATRIX | COMMON POINT | APPROXIMATION | ALGORITHM | MATLAB SOFTWARE PACKAGE | Algorithms | approximation | Naturvetenskap | Low-rank | Natural Sciences | Matematik
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 6/2018, Volume 24, Issue 3, pp. 719 - 758
Journal Article
Mathematical programming, ISSN 1436-4646, 2016, Volume 162, Issue 1-2, pp. 537 - 548
Journal Article
Numerical Algorithms, ISSN 1017-1398, 8/2016, Volume 72, Issue 4, pp. 1021 - 1042
.... Of the available methods with guaranteed convergence to the unique solution of this problem the easiest to implement, and perhaps the most widely used, is the alternating projections method... 
Nearest correlation matrix | Numeric Computing | Theory of Computation | Algorithms | Algebra | 15A57 | Numerical Analysis | 65F30 | Computer Science | Alternating projections method | Anderson acceleration | Dykstra’s correction | Positive semidefinite matrix | Indefinite matrix | CONVERGENCE ACCELERATION | MATHEMATICS, APPLIED | ALGORITHM | Dykstra's correction | INVERSE
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 10/2020, Volume 603, pp. 41 - 56
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections... 
Alternating projection method | Principal angles | Oppenheim angle | Linear projections | Mathematics - Functional Analysis
Journal Article
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 06/2012, Volume 21, Issue 7, pp. 1250069 - 1250017
The paper addresses the enumeration problem for k-tangles. We introduce the notion of a cascade diagram of a k-tangle projection and suggest an effective enumeration algorithm for projections based on the cascade representation... 
MATHEMATICS | Tangles | LINKS | CLASSIFICATION | alternating tangles | PRIME ALTERNATING KNOTS | k-tangle enumeration | Algorithms | Pictures | Enumeration | Cascades | Projection | Knot theory | Representations
Journal Article
JOURNAL OF CONVEX ANALYSIS, ISSN 0944-6532, 2016, Volume 23, Issue 3, pp. 823 - 847
We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems... 
Alternating projections | MATHEMATICS | subdifferential | normal cone | DIFFERENTIABILITY | STATIONARITY | uniform regularity
Journal Article
Optics and lasers in engineering, ISSN 0143-8166, 2019, Volume 121, pp. 96 - 103
....•The proposed method is aimed at the retrieval of high-resolution phase pattern.•The proposed method is based on a hybrid of PhaseCut and alternating projection... 
Alternating projection | PhaseCut | Diffraction intensity | Phase retrieval | Extrapolative method | RECOVERY | RECONSTRUCTION | ALGORITHM | OPTICS | Algorithms | Numerical analysis | Mechanical engineering | Methods
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 7/2015, Volume 166, Issue 1, pp. 213 - 233