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Revisiting Performance of BiCGStab Methods for Solving Systems with Multiple Right-Hand Sides

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Boris Krasnopolsky

Numerical Analysis · Submitted 30 Jul 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The proposed merging of vector operations allows to reduce the memory traffic and improve performance of the calculations by about 30%.

how it is stated · asserted 0.94 read the record →

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arXiv ID1907.12874 (version 3)
Pith IDJM4NSECZ, Pith's permanent record of this paper and its review
CitationBoris Krasnopolsky. "Revisiting Performance of BiCGStab Methods for Solving Systems with Multiple Right-Hand Sides." arXiv:1907.12874 (2019). https://pith.science/paper/JM4NSECZ
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,466 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.34 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse matrices. The paper presents execution time analytical model for the time to solve the systems. The BiCGStab method and several modifications including the Reordered BiCGStab and Pipelined BiCGStab methods are analyzed and the range of applicability for each method providing the best execution time is highlighted. The results of the analytical model are validated by the numerical experiments and compared with results of other authors. The presented results demonstrate an increasing role of the vector operations when performing simulations with multiple right-hand side vectors. The proposed merging of vector operations allows to reduce the memory traffic and improve performance of the calculations by about 30%.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. contribution 0.53 0.48 0.04 asserted 0.89
s1 These iterative methods are widely used for solving systems with large sparse matrices. background 1.00 0.05 0.02 asserted 1.00
s2 The paper presents execution time analytical model for the time to solve the systems. contribution 0.50 0.90 0.05 asserted 0.99
s3 The BiCGStab method and several modifications including the Reordered BiCGStab and Pipelined BiCGStab methods are analyzed and the range of applicability for each method providing the best execution time is highlighted. contribution 0.70 0.89 0.47 asserted 1.00
s4 The results of the analytical model are validated by the numerical experiments and compared with results of other authors. method 0.85 0.91 0.06 asserted 0.99
s5 The presented results demonstrate an increasing role of the vector operations when performing simulations with multiple right-hand side vectors. result 0.60 0.82 0.22 asserted 1.00
s6 The proposed merging of vector operations allows to reduce the memory traffic and improve performance of the calculations by about 30%. result 0.93 0.89 0.53 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 0.69 · evidence from simulation or computation 0.70.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse matrices. The paper presents execution time analytical model for the time to solve the systems. The BiCGStab method and several modifications including the Reordered BiCGStab and Pipelined BiCGStab methods are analyzed and the range of applicability for each method providing the best execution time is highlighted. The results of the analytical model are validated by the numerical experiments and compared with results of other authors. The presented results demonstrate an increasing role of the vector operations when performing simulations with multiple right-hand side vectors. The proposed merging of vector operations allows to reduce the memory traffic and improve performance of the calculations by about 30%.

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