A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS \(L^2\) spaces
DOI10.1007/s43036-020-00079-1zbMath1444.47078arXiv1904.04414OpenAlexW2937082426MaRDI QIDQ782544
James Tian, Myung-Sin Song, Palle E. T. Jorgensen
Publication date: 27 July 2020
Published in: Advances in Operator Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1904.04414
Hilbert spaceiterated function systemframesSierpinski gasketinfinite productsKaczmarz algorithmanalysis/synthesisrandomized Kaczmarz algorithm
Algebras of unbounded operators; partial algebras of operators (47L60) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Numerical methods for integral transforms (65R10) General harmonic expansions, frames (42C15) Applications of functional analysis in quantum physics (46N50) Applications of functional analysis in probability theory and statistics (46N30)
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- The unconditional constants for Hilbert space frame expansions
- Acceleration of randomized Kaczmarz method via the Johnson-Lindenstrauss lemma
- Kaczmarz algorithm in Hilbert space and tight frames
- Fourier frequencies in affine iterated function systems
- Fusion frames and distributed processing
- \(V\)-variable fractals: Fractals with partial self similarity
- A randomized Kaczmarz algorithm with exponential convergence
- Analycity properties of the characteristic exponents of random matrix products
- Characteristic exponents and invariant manifolds in Hilbert space
- System bandwidth and the existence of generalized shift-invariant frames
- Markov chains and generalized wavelet multiresolutions
- Infinite-dimensional measure spaces and frame analysis
- Dilations of operator-valued measures with bounded \(p\)-variations and framings on Banach spaces
- A new greedy Kaczmarz algorithm for the solution of very large linear systems
- A nonstationary accelerating alternating direction method for frame-based Poissonian image deblurring
- A characterization of boundary representations of positive matrices in the Hardy space via the Abel product
- Robust subspace clustering
- Positive matrices in the Hardy space with prescribed boundary representations via the Kaczmarz algorithm
- Duality and geodesics for probabilistic frames
- Convergence rates for Kaczmarz-type algorithms
- Introducing the windowed Fourier frames technique for obtaining the approximate solution of the coupled system of differential equations
- Convolutional frames and the frame potential
- On the nature of turbulence
- A hybrid Kaczmarz-conjugate gradient algorithm for image reconstruction
- On equivalence of infinite product measures
- On the Kaczmarz algorithm of approximation in infinite-dimensional spaces
- Projections and preconditioning for inconsistent least-squares problems
- KACZMARZ ALGORITHM AND FRAMES
- Non-commutative Analysis
- Asymptotics of eigenvalue clusters for Schrödinger operators on the Sierpiński gasket
- Self-calibration and biconvex compressive sensing
- Iterated Products of Projections in Hilbert Space
- Entropy encoding, Hilbert space, and Karhunen-Loève transforms
- The Projected Power Method: An Efficient Algorithm for Joint Alignment from Pairwise Differences
- Admissible sequences of positive operators
- Kaczmarz algorithm in Hilbert space
- The Kaczmarz algorithm, row action methods, and statistical learning algorithms
- A matrix characterization of boundary representations of positive matrices in the Hardy space
- 𝑊-Markov measures, transfer operators, wavelets and multiresolutions
- Thermodynamic Formalism
- A Norm Convergence Result on Random Products of Relaxed Projections in Hilbert Space
- Robustness of fusion frames under erasures of subspaces and of local frame vectors
- Probabilistic Frames: An Overview
- A subspace method for space time adaptive processing
- Preconditioning techniques in frame theory and probabilistic frames
- Theory of Reproducing Kernels
- Notes on infinite product measure spaces, I
- Phase Retrieval via Matrix Completion
- Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm
