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BiCGStab(ℓ) #134

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merged 10 commits into from Jul 14, 2017

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haampie commented Jul 6, 2017

This is still a work in progress version of BiCGStab(ℓ). It is based on the original article, uses BLAS and includes left preconditioning.

Todo:

  • Incorporate the convergence history stuff.
  • Improvement of [1]
  • Improvement of [2]

[1] Sleijpen, Gerard LG, and Henk A. Vorst. "Maintaining convergence properties of BiCGstab methods in finite precision arithmetic." Numerical Algorithms 10.2 (1995): 203-223.
[2] Sleijpen, G. LG, and Henk A. van der Vorst. "Reliable updated residuals in hybrid Bi-CG methods." Computing 56.2 (1996): 141-163.

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codecov-io Jul 6, 2017

Codecov Report

Merging #134 into master will increase coverage by 0.21%.
The diff coverage is 89.47%.

Impacted file tree graph

@@            Coverage Diff             @@
##           master     #134      +/-   ##
==========================================
+ Coverage   84.97%   85.19%   +0.21%     
==========================================
  Files          19       20       +1     
  Lines        1478     1554      +76     
==========================================
+ Hits         1256     1324      +68     
- Misses        222      230       +8
Impacted Files Coverage Δ
src/bicgstabl.jl 89.47% <89.47%> (ø)

Continue to review full report at Codecov.

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Δ = absolute <relative> (impact), ø = not affected, ? = missing data
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codecov-io commented Jul 6, 2017

Codecov Report

Merging #134 into master will increase coverage by 0.21%.
The diff coverage is 89.47%.

Impacted file tree graph

@@            Coverage Diff             @@
##           master     #134      +/-   ##
==========================================
+ Coverage   84.97%   85.19%   +0.21%     
==========================================
  Files          19       20       +1     
  Lines        1478     1554      +76     
==========================================
+ Hits         1256     1324      +68     
- Misses        222      230       +8
Impacted Files Coverage Δ
src/bicgstabl.jl 89.47% <89.47%> (ø)

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 9e435ba...5fe54d9. Read the comment docs.

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haampie Jul 11, 2017

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At the moment I don't think it is completely necessary to implement the improvements from the papers. The thing is there is no standard implementation of BiCGStab(ℓ) and there's a lot of freedom.

The current implementation works fine for moderate values of . if someone wants to use large and still have enough precision, then it's a good idea to switch to a fancy implementation that solves the polynomial part using Gram-Schmidt rather than normal equations and once in a while recomputes the exact residual.

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haampie commented Jul 11, 2017

At the moment I don't think it is completely necessary to implement the improvements from the papers. The thing is there is no standard implementation of BiCGStab(ℓ) and there's a lot of freedom.

The current implementation works fine for moderate values of . if someone wants to use large and still have enough precision, then it's a good idea to switch to a fancy implementation that solves the polynomial part using Gram-Schmidt rather than normal equations and once in a while recomputes the exact residual.

@haampie haampie referenced this pull request Jul 11, 2017

Closed

Added bicgstab #4

@haampie haampie changed the title from WIP BiCGStab(ℓ) to BiCGStab(ℓ) Jul 14, 2017

@andreasnoack andreasnoack merged commit eacea1a into JuliaMath:master Jul 14, 2017

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coverage/coveralls Coverage increased (+0.2%) to 85.199%
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