Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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AN ITERATIVE METHOD FOR SYMMETRIC INDEFINITE LINEAR SYSTEMS

  • Walker, Homer-F. (Department of Mathematical Sciences Worcester Polytechnic Institute) ;
  • Yi, Su-Cheol (Department of Applied Mathematics Changwon National University)
  • Published : 2004.04.01
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Abstract

For solving symmetric systems of linear equations, it is shown that a new Krylov subspace method can be obtained. The new approach is one of the projection methods, and we call it the projection method for convenience in this paper. The projection method maintains the residual vector like simpler GMRES, symmetric QMR, SYMMLQ, and MINRES. By studying the quasiminimal residual method, we show that an extended projection method and the scaled symmetric QMR method are equivalent.

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References

  1. Numer. Math. v.60 QMR:a quasi-minimal residual method for non-Hermitian linear systems R.W.Freund;N.M.Nachtigal https://doi.org/10.1007/BF01385726
  2. ORNL/TM-12754 A new Krylov subspace method for symmetric indefinite linear systems
  3. Tech. Rep. 91-26 A quasi-minimal residual squared algorithm for non Hermitian linear systems R.W.Freund;H.Szeto
  4. Murray Hill Bell Labs Simplifications of the nonsymmetric Lanczos process and a new algorithm for Hermitian indefinite linear systems R.W.Freund;H.Zha
  5. Matrix Computations G.H.Golub;C.F.Van Loan
  6. SIAM J. Numer. Anal. v.12 Solution of sparse indefinite systems of linear equations C.C.Paige;M.A.Saunders https://doi.org/10.1137/0712047
  7. SIAM J. Sci. Stat. Comput. v.7 GMRES:A generalized minimal residual algorithm for solving nonsymmetric linear systems Y.Saad;M.H.Schultz https://doi.org/10.1137/0907058
  8. Numer. Lin. Alg. Appl. v.1 A simple GMRES H.F.Walker;Lu Zhou https://doi.org/10.1002/nla.1680010605