Plan for adding Conjugate Residual (CR) type methods for linear systems
Dear all, I resubmitted a PR to support Conjugate Residual (CR) method in gh-14675: https://github.com/scipy/scipy/pull/14675 which is a light-weight solver and can be used in symmetric indefinite or Hermitian systems. The algorithm is formally similar to Conjugate Gradient (CG) but mathematically equivalent to Minimal Residual (MINRES). For symmetric positive-definite problems, CR has the same convergence as CG. But for symmetric indefinite problems, CR has almost the same iterative steps and less computation in each iteration than MINRES, which means higher computational efficiency. The arrival of CR algorithm will further enrich the reentrant Krylov subspace methods implemented in SciPy and give users more/better choices. The PR is only a part of CR type methods which will include CR, Bi-CR, Generalized CR and GCRO-DR etc. This large class of algorithms are widely used in some specific problems and play an important role. So we have implemented CR in this PR firstly, and then we will continue to implement Bi-CR and GCRO-DR methods respectively. The PR used the functional features of NumPy and SciPy to implement the CR method. Hope you like it and look forward to your review. Thank you all. Best Regards, Gang
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赵刚