Pivoting Strategy for Fast LU Decomposition of Sparse Block Matrices

2017 ◽  
Keyword(s):  
Lu Decomposition ◽  
Block Matrices

Localization Algorithm of Sparse Targets Based on LU-decomposition

2014 ◽  
Vol 35 (9) ◽  
pp. 2234-2239 ◽  
Author(s):  
Chun-hui Zhao ◽  
Yun-long Xu ◽  
Hui Huang
Keyword(s):  
Lu Decomposition ◽  
Localization Algorithm

Representations for the image-kernel (p,q)-inverses of block matrices in rings

2020 ◽  
Vol 27 (2) ◽  
pp. 297-305
Author(s):  
Dijana Mosić
Keyword(s):  
Block Matrix ◽  
Block Matrices ◽  
Schur Form

AbstractWe present the conditions for a block matrix of a ring to have the image-kernel{(p,q)}-inverse in the generalized Banachiewicz–Schur form. We give representations for the image-kernel inverses of the sum and the product of two block matrices. Some characterizations of the image-kernel{(p,q)}-inverse in a ring with involution are investigated too.

Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Leonid L. Frumin
Keyword(s):  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Numerical Algorithms ◽  
Scattering Problems ◽  
Block Matrices ◽  
Nonlinear Schrödinger ◽  
Direct Scattering ◽  
Vector Case ◽  
Manakov Model ◽  
Vector Variant

AbstractWe introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem’s efficient numerical algorithms to the vector case. The inversion of block matrices of the discretized system of Gelfand–Levitan–Marchenko integral equations solves the inverse scattering problem using the vector variant the Toeplitz Inner Bordering algorithm of Levinson’s type. The reversal of steps of the inverse problem algorithm gives the solution of the direct scattering problem. Numerical tests confirm the proposed vector algorithms’ efficiency and stability. We also present an example of the algorithms’ application to simulate the Manakov vector solitons’ collision.

Euclidean norm estimates of the inverse of some special block matrices

2016 ◽  
Vol 284 ◽  
pp. 12-23 ◽  
Author(s):  
Ljiljana Cvetković ◽  
Vladimir Kostić ◽  
Ksenija Doroslovački ◽  
Dragana Lj. Cvetković
Keyword(s):  
Euclidean Norm ◽  
Block Matrices ◽  
Norm Estimates

Special parallel processor for lu decomposition of a large-scale sparse matrix

1987 ◽  
Vol 18 (6) ◽  
pp. 89-99 ◽  
Author(s):  
Hideki Asai ◽  
Mitsuo Asai ◽  
Mamoru Tanaka
Keyword(s):  
Large Scale ◽  
Sparse Matrix ◽  
Lu Decomposition ◽  
Parallel Processor
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