Editorial:–––––BEGIN GEEK CODE BLOCK––––– Version: 3.1 GCC/P/SS d? s++:++ a C++(+++) ULU++++ P L E---- W+++ N++ o-- K- w O M V PS+ PE++ Y PGP- t- 5-- X-- R- !tv b++++ DI+++ D-- G++ e+++ h++ r+ !z+ Version: 3.1 GCC/P/SS d? s++:++ a C++(+++) ULU++++ P L E---- W+++ N++ o-- K- w O M V PS+ PE++ Y PGP- t- 5-- X-- R- !tv b++++ DI+++ D-- G++ e+++ h++ r+ !z+–––––END GEEK CODE BLOCK–––––

Frank Romeike

doi:10.1002/risk.200490053

Editorial:–––––BEGIN GEEK CODE BLOCK––––– Version: 3.1 GCC/P/SS d? s++:++ a C++(+++) ULU++++ P L E---- W+++ N++ o-- K- w O M V PS+ PE++ Y PGP- t- 5-- X-- R- !tv b++++ DI+++ D-- G++ e+++ h++ r+ !z+ Version: 3.1 GCC/P/SS d? s++:++ a C++(+++) ULU++++ P L E---- W+++ N++ o-- K- w O M V PS+ PE++ Y PGP- t- 5-- X-- R- !tv b++++ DI+++ D-- G++ e+++ h++ r+ !z+–––––END GEEK CODE BLOCK–––––

RISKNEWS ◽

10.1002/risk.200490053 ◽

2004 ◽

Vol 1 (3) ◽

pp. 3-3

Author(s):

Frank Romeike

Keyword(s):

Block Version

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The block version of the reflection method for the solution of linear algebraic systems

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(70)90052-2 ◽

1970 ◽

Vol 10 (5) ◽

pp. 265-271

Author(s):

V.V. Voevodin ◽

T.L. Rudneva

Keyword(s):

Reflection Method ◽

Algebraic Systems ◽

Linear Algebraic Systems ◽

Block Version

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A New Algorithm for Solving Large-Scale Generalized Eigenvalue Problem Based on Projection Methods

Mathematical Problems in Engineering ◽

10.1155/2020/8895856 ◽

2020 ◽

Vol 2020 ◽

pp. 1-10

Author(s):

F. Abbasi Nedamani ◽

A. H. Refahi Sheikhani ◽

H. Saberi Najafi

Keyword(s):

Numerical Stability ◽

Large Scale ◽

Eigenvalue Problems ◽

Projection Methods ◽

Generalized Eigenvalue ◽

Generalized Eigenvalue Problems ◽

Ritz Procedure ◽

The Moment ◽

Block Version ◽

Methods Numerical

In this paper, we consider four methods for determining certain eigenvalues and corresponding eigenvectors of large-scale generalized eigenvalue problems which are located in a certain region. In these methods, a small pencil that contains only the desired eigenvalue is derived using moments that have obtained via numerical integration. Our purpose is to improve the numerical stability of the moment-based method and compare its stability with three other methods. Numerical examples show that the block version of the moment-based (SS) method with the Rayleigh–Ritz procedure has higher numerical stability than respect to other methods.

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Aspects for a block version of the interval Cholesky algorithm

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(02)00725-2 ◽

2003 ◽

Vol 152 (1-2) ◽

pp. 481-491 ◽

Cited By ~ 3

Author(s):

Uwe Schäfer

Keyword(s):

Block Version

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A block version algorithm to approximate inverse factors

Applied Mathematics and Computation ◽

10.1016/j.amc.2004.03.024 ◽

2005 ◽

Vol 162 (3) ◽

pp. 1499-1509 ◽

Cited By ~ 2

Author(s):

D.Khojasteh Salkuyeh ◽

F. Toutounian

Keyword(s):

Approximate Inverse ◽

Block Version

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A Block Version of Orthogonal Rotations for Improving the Accuracy of Hybrid State Estimators

IEEE Transactions on Power Systems ◽

10.1109/tpwrs.2020.2991863 ◽

2020 ◽

Vol 35 (6) ◽

pp. 4432-4444

Author(s):

Daniel Martins Bez ◽

Antonio Simoes Costa ◽

Larah Bruning Ascari ◽

Edson Zanlorensi Junior

Keyword(s):

Hybrid State ◽

State Estimators ◽

Block Version

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Bilus: A block version of ilus factorization

Journal of Applied Mathematics and Computing ◽

10.1007/bf02935763 ◽

2004 ◽

Vol 15 (1-2) ◽

pp. 299-312 ◽

Cited By ~ 2

Author(s):

Davod Khojasteh Salkuyeh ◽

Faezeh Toutounian

Keyword(s):

Block Version

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Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33015033 ◽

2019 ◽

Vol 33 ◽

pp. 5033-5040 ◽

Cited By ~ 3

Author(s):

Tao Sun ◽

Penghang Yin ◽

Dongsheng Li ◽

Chun Huang ◽

Lei Guan ◽

...

Keyword(s):

Linear Convergence ◽

Objective Functions ◽

Step Size ◽

Decentralized Optimization ◽

Strongly Convex ◽

Update Rules ◽

Block Version ◽

Convex Setting ◽

Convex Condition ◽

Made In

In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a relaxed strongly convex condition, the linear convergence is established under weaker assumptions on the step size and inertial parameter than made in the existing literature. We extend our results to multi-block version of the algorithm with both the cyclic and stochastic update rules. In addition, our results can also be extended to decentralized optimization, where the ergodic analysis is not applicable.

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Block Power Method for SVD Decomposition

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.1515/auom-2015-0024 ◽

2015 ◽

Vol 23 (2) ◽

pp. 45-58 ◽

Cited By ~ 3

Author(s):

A. H. Bentbib ◽

A. Kanber

Keyword(s):

Singular Values ◽

Diagonal Matrix ◽

New Method ◽

Power Method ◽

Orthogonal Matrices ◽

Singular Vectors ◽

Left And Right ◽

Svd Decomposition ◽

Block Version

Abstract We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈ Rn×m. Our approach is based on using a block version of the Power Method to compute an k-block SV D decomposition: Ak = Uk∑kVkT , where ∑k is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ1≥ σ2 ⋯ ≥ σk. Uk and Vk are orthogonal matrices whose columns are the left and right singular vectors of the k largest singular values. This approach is more efficient as there is no need of calculation of all singular values. The QR method is also presented to obtain the SV D decomposition.

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