Search Results - block triangular solves

Developing a Multi-GPU-Enabled Preconditioned GMRES with Inexact Triangular Solves for Block Sparse Matrices by Ma, Wenpeng, Hu, Yiwen, Yuan, Wu, Liu, Xiazhen

“… In this paper, we propose and implement an iterative, inexact block triangular solve on multi-GPUs based on PETSc’s framework…”
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Communication Avoiding Block Low-Rank Parallel Multifrontal Triangular Solve with Many Right-Hand Sides by Amestoy, Patrick, Boiteau, Olivier, Buttari, Alfredo, Gerest, Matthieu, Jézéquel, Fabienne, L’Excellent, Jean-Yves, Mary, Theo

“… In this paper, we investigate the performance of the BLR triangular solve phase, which we observe to be underwhelming when dealing with many right-hand sides (RHS…”
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A Comparative Study of Block Incomplete Sparse Approximate Inverses Preconditioning on Tesla K20 and V100 GPUs by Ma, Wenpeng, Yuan, Wu, Liu, Xiazhen

“… (Tesla K20 and Tesla V100). Block–Jacobi preconditioning with Block–ISAI (BJPB-ISAI) shows an advantage over the level-scheduling based triangular solves from the cuSPARSE library for the cases, and the overhead of setting up Block–ISAI and the total wall clock times of GMRES is greatly reduced using Tesla V100 GPUs compared to Tesla K20 GPUs…”
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Fast synchronization‐free algorithms for parallel sparse triangular solves with multiple right‐hand sides by Liu, Weifeng, Li, Ang, Hogg, Jonathan D., Duff, Iain S., Vinter, Brian

“…Summary The sparse triangular solve kernels, SpTRSV and SpTRSM, are important building blocks for a number of numerical linear algebra routines…”
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On block triangular preconditioned iteration methods for solving the Helmholtz equation by Lang, Chao, Gao, Rong, Qiu, Chujun

“… triangular preconditioners are presented to solve a block two-by-two linear system derived from the discrete Helmholtz equation…”
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The Best Reduction of Matrices to Block-Triangular Form for Hierarchical Decomposition Problems by Bazilevich, Yu. N.

“…The author solves the problem of reducing several complex (generally speaking) n × n matrices to the same block-triangular form with a maximum possible number of blocks on the main diagonal with the use of a similarity transformation…”
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Parallel algorithms for solving linear systems with sparse triangular matrices by Mayer, Jan

“… The first algorithm solves the triangular matrix by block anti-diagonals. The drawback of this approach is that it can be difficult to choose an appropriate block structure…”
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Approximate inversion method for time‐fractional subdiffusion equations by Lu, Xin, Pang, Hong‐Kui, Sun, Hai‐Wei, Vong, Seak‐Weng

“…‐scale linear system with a block lower triangular Toeplitz coefficient matrix. The approximate inversion method is employed to solve this system…”
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A new block triangular preconditioner for three-by-three block saddle-point problem by Li, Jun, Xiong, Xiangtuan

“…In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT…”
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Triangular intuitionistic fuzzy linear system of equations with applications: an analytical approach by Shams, Mudassir, Kausar, Nasreen, Agarwal, Praveen, Shah, Mohd Asif

“… The Block Homotopy Modified Perturbation Method is found to be efficient and practical to solve $ n \times n $ n…”
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Modified Newton-PSBTS method for solving complex nonlinear systems with symmetric Jacobian matrices by Zhang, Yuanyuan, Wu, Qingbiao, Feng, Yuye, Xiao, Yao

“… triangular splitting (MN-PSBTS) iteration method. In order to obtain the solution of complex nonlinear systems with symmetric Jacobian matrix, by employing the preconditioned symmetric block triangular splitting (PSBTS…”
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A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation by Lin, Xue-lei, Lu, Xin, Ng, Micheal K., Sun, Hai-Wei

“… Using the finite difference discretization of fractional time derivative, a block lower triangular Toeplitz matrix is obtained where each main diagonal block contains a two-dimensional matrix for the Laplacian operator…”
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A new approximation of the Schur complement in preconditioners for PDE-constrained optimization by Pearson, John W., Wathen, Andrew J.

“… Block diagonal and block triangular preconditioners have previously been designed to be used to solve such problems along with MINRES and non…”
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Adaptive Fuzzy Control With Prescribed Performance for Block-Triangular-Structured Nonlinear Systems by Li, Yongming, Tong, Shaocheng

“…In this paper, an adaptive fuzzy control method with prescribed performance is proposed for multi-input and multioutput block-triangular-structured nonlinear systems with immeasurable states…”
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A Preconditioned MINRES Method for Block Lower Triangular Toeplitz Systems by Li, Congcong, Lin, Xuelei, Hon, Sean, Wu, Shu-Lin

“…In this study, a novel preconditioner based on the absolute-value block α -circulant matrix approximation is developed, specifically designed for nonsymmetric dense block lower triangular Toeplitz (BLTT…”
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The g-Drazin inverses of anti-triangular block operator matrices by Chen, Huanyin, Sheibani, Marjan

“…An element a in a Banach algebra A has g-Drazin inverse if there exists b∈A such that ab=ba,b=bab and a−a2b∈Aqnil. In this paper we find new explicit representations of the g-Drazin inverse of the block operator matrix…”
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Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning by Chow, Edmond, Anzt, Hartwig, Scott, Jennifer, Dongarra, Jack

“…When using incomplete factorization preconditioners with an iterative method to solve large sparse linear systems, each application of the preconditioner involves solving two sparse triangular systems…”
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A block upper triangular splitting method for solving block three-by-three linear systems arising from the large indefinite least squares problem by Li, Jun, Xin, Kailiang, Meng, Lingsheng

“…, then a block upper triangular matrix splitting of the coefficient matrix of the block three-by-three linear systems is given, the splitting not only produces the stationary iteration method, but also…”
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Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub-diffusion equations by Lu, Xin, Pang, Hong-Kui, Sun, Hai-Wei

“…SummaryA fast approximate inversion method is proposed for the block lower triangular Toeplitz with tri‐diagonal blocks (BL3TB) matrix…”
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Optimal Sequence in General Flow Shop with Job Block Criteria using Fuzzy Index Technique

“… The parameters required to solve such problem was considered to be in triangular fuzzy number. The concept of job block concept has been introduced to understand relative interference of one job…”
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