Convergence of block iterative methods applied to sparse least-squares problems
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TLDR
New results are obtained, giving the exact convergence and divergence domains for such iterative applications of the block-SOR iterative method to a consistently ordered block-Jacobi matrix that is weakly cyclic of index 3.About:
This article is published in Linear Algebra and its Applications.The article was published on 1984-04-01 and is currently open access. It has received 56 citations till now. The article focuses on the topics: Iterative method & Overdetermined system.read more
Citations
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Successive overrelaxation (SOR) and related methods
TL;DR: In this paper, both the point and block SOR methods are considered for the solution of a linear system of the form Ax=b, where A∈ C n,n and b∈ c n ⧹{0}.
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On the solution of singular linear systems of algebraic equations by semiiterative methods
TL;DR: In this paper, the authors investigated the solution of the linear fixed point problemx=Tx+c by applying semi-iterative methods (SIM's) to the basic iterationx0∈ℂn,xk≔Tck−1+c(k≧1).
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Block SOR methods for rank-deficient least-squares problems
TL;DR: A 2-block SOR method and a 3-blockSOR method are proposed to solve the rank-deficient problem and the convergence of the block SOR methods is studied.
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Convergence of a direct-iterative method for large-scale least-squares problems
TL;DR: In this article, a 2-cyclic block SOR method was proposed to solve the least square problem in geodesy, where A1 is easily formed and is large and sparse.
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Least-squares solution of overdetermined inconsistent linear systems using Kaczmarz's relaxation
TL;DR: Two iterative algorithms which generate sequences convergent to the minimal Euclidean length solution in the general case (inconsistent system and rank deficient matrix) and need no special assumptions about the system.
References
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Book
Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Book
Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
Journal ArticleDOI
Large scale geodetic least squares adjustment by dissection and orthogonal decomposition
Gene H. Golub,Robert J. Plemmons +1 more
TL;DR: In this article, a block-orthogonal decomposition method was used in conjunction with a nested dissection scheme to solve the least square adjustment problem in large-scale matrix problems.
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The analysis ofk-step iterative methods for linear systems from summability theory
TL;DR: In this article, a regionS of the complex plane is determined such that a two-step iterative method converges if the eigenvalues of an iteration operatorT are contained inS. For a givenS, optimal methods are described, and upper and lower bounds are derived for the associated asymptotic rate of convergence.