Applied Iterative Methods

By Charles L. Byrne. 2007

348 citations recorded by the source corpus.

Subfields: Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/b8c1ae8ae3f2ff37f4e7675d29fc34fe4c1dbd0b

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In Mathematical Physics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Paved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method (2012, methodology): “czmarz method was originally introduced in the paper [Kac37]. It was reinvented by researchers in tomography [GBH70] under the appellation “algebraic reconstruction technique” (ART). See Byrne’s book [Byr08] for a contemporary summary of this literature. The classical variants of the Kaczmarz method”
Convergence Analysis of Inexact Randomized Iterative Methods (2019, methodology): “sic simplies to x k+1 = x k !I :C(I > :CAI :C) yI> :C(Ax k b) + k: (22) For more papers related to Kaczmarz method (randomized, greedy, cyclic update rules) we refer the interested reader to [23,28,38,5,37,39,9,33,34,13,31,59,35,50]. For the coordinate descent method (a.k.a Gauss-Seidel for l”
Rows vs. Columns: Randomized Kaczmarz or Gauss-Seidel for Ridge Regression (2015, methodology): “The Kaczmarz method [11] is also known in the tomography setting as the Algebraic Reconstruction Technique (ART) [6, 15, 1, 9].”
Price-Based Spectrum Management in Cognitive Radio Networks (2007, methodology): “The parallel PIWF algorithm is related to theJacobi computational procedure [9], where in each iteration CR users simultaneously perform price-based water-filling based on the interference generated by the other users in the previous iterations.”
Numerical Methods for Elliptic and Parabolic Partial Differential Equations (2003, neutral): “[18] L.”
Momentum and stochastic momentum for stochastic gradient, Newton, proximal point and subspace descent methods (2017, methodology): “ selects the rows to project onto in a cyclic manner. In practice, many dierent selection rules can be adopted. For non-random selection rules (cyclic, greedy, etc) we refer the interested reader to [56,5,50,57,8]. In this work we are interested in randomized variants of the Kaczmarz method, rst ana”
Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm (2013, positive): “otic convergence rates, showing that drawingrowsproportionallytokaik2 2 leadsto provableexponentialconvergence inexpectation[36]. Recent works use acceleration techniques to improve convergence rates [18, 27, 9, 31, 41, 10, 8, 5, 28, 29, 30, 23, 22]. However, one can easily verify that the iterates ”
Randomized Iterative Methods for Linear Systems: Momentum, Inexactness and Gossip (2019, methodology): “For non-random selection rules (cyclic, greedy, etc) we refer the interested reader to [158, 17, 144, 159, 27].”
Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems (2007, neutral): “(For example, see [37], [42], [96], [106].”
Chebyshev semi-iteration in preconditioning for problems including the mass matrix. (2008, methodology): “The Chebyshev semi-iterative method was developed by Golub and Varga [12], [13, Section 10.1.5], and also Young [15] .”