Matrix Iterative Analysis

By R. Varga, J. Gillis. 1961

Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.

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Citations in the corpus

On Convergence of Emphatic Temporal-Difference Learning (2015, methodology): “Let θ∗ denote the desired limit for ETD(λ): θ∗ = −C−1b, for C, b defined by Eq.”
Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization (2017, methodology): “Strategies of this form are known as over-relaxation in the numerical analysis literature [26] and as Nesterov acceleration in the optimization literature [27].”
Codes for mass data storage systems (2004, methodology): “The existence of a positive eigenvalue and corresponding eigenvector with positive elements is guaranteed by the Perron-Frobenius theorems [325].”
An introduction to continuous optimization for imaging (2016, methodology): “R. S. Varga (1962), Matrix Iterative Analysis, Prentice Hall.”
Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity (2009, background): “I thank Gauthier Sallet for bringing the results by Varga [43] to my attention and two anonymous referees for their helpful remarks.”
Linear Time Average Consensus on Fixed Graphs and Implications for Decentralized Optimization and Multi-Agent Control (2014, unknown): “ the convergence speed of iterative methods linear systems can be sped up by an order of magnitude by taking steps with \momentum" is very old; see, for example, chapters 4 and 5 of the textbook [48]. Within the context of distributed computation, the rst paper, to our knowledge, to make use of”
M-Tensors and Some Applications (2014, unknown): “The concept ofM -matrices, which have many applications in various fields such as computational mathematics, mathematical physics, mathematical economics, graph theory, and wireless communications [1, 10, 14, 24], was introduced by Ostrowski [21] in 1937 [1, 10, 14, 25].”
Asymptotic properties of consensus-type algorithms for networked systems with regime-switching topologies (2011, unknown): “The reader is referred to Brualdi and Ryser (1991) for basic matrix properties in graphs and to Varga (2000) for matrix iterative schemes.”
Solving nonlinear matrix equations arising in Tree-Like stochastic processes (2003, unknown): “If Bn 0 and ρ(Bn) < 1 then I − Bn is a nonsingular M-matrix, therefore, for the properties of M-matrices [16], the more convenient choice for r is the one for which ‖ArŜ−1 n ‖ · ‖Ŝ−1Dr‖ is maximum for a given norm ‖ · ‖.”
The convergence of TD(λ) for general λ (1992, unknown): “By another theorem of Varga (1962) l im [I - o~XTXD(I - (1 - X)Q[I - XQ]-~)] n = 0.”