Bibliography for Iterative Refinement

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  1. A Modified Iterative Refinement Scheme  
    Achiya Dax
    SIAM Journal on Scientific Computing, Volume 25, Number 4, 2003, pp. 1199-1213.
  2. Iterative refinement of solution with biparameter for solving ill-conditioned systems of linear algebraic equations
    Wu X.-y.; Shao R.; Xue G.-h.
    Applied Mathematics and Computation, 25 September 2002, vol. 131, no. 2, pp. 235-244(10), Ingenta.  
  3. Refined subspace iteration algorithm for large sparse eigenproblems
    Jia, Zhongxiao  
    Applied Numerical Mathematics, v 32, n 1, Jan, 2000, p 35-52, Compendex.
  4. An improved algorithm for the iterative refinement method.
    Al-Towaiq, M. H.
    J. Discrete Math. Sci. Cryptography 2 (1999), no. 1, 73--76, MathSciNet.  
  5. Iterative refinement using splitting methods
    Yuan, Jin Yun  
    Linear Algebra and Its Applications, v 273, n 1-3, Apr 1, 1998, p 199-214, Compendex.
  6. A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems
    Jia, Zhongxiao  
    Linear Algebra and Its Applications, v 270, n 1-3, February, 1998, p 171-189, Compendex.
  7. Modified iterative refinement algorithm for efficient solution of parameter-dependent sets of linear equations
    Simon, Peter S.; Kenney, Charles S.; McInturff, Kim; Jobsky, Robert W.; Bryan, Thomas A.
    IEEE Antennas and Propagation Society, AP-S International Symposium (Digest), v 3, 1998, p 1510-1513, Compendex.
  8. Iterative Refinement and LAPACK  PDF    
    Higham, Nicholas J.
    IMA J. Numer. Anal. 17 (1997), no. 4, 495--509, MathSciNet.  
  9. A note on the convergence of the Weierstrass sor method for polynomial roots.
    Petkovic, M.S.; Kjurkchiev, N.
    Journal of computational and applied mathematics, 1997, vol. 80, no. 1, pp. 163, Ingenta.
  10. Iterative refinement of the singular-value decomposition solution to the regression equations
    Henshall J.M.; Smith D.M.
    Computational Statistics and Data Analysis, 23 October 1996, vol. 22, no. 6, pp. 573-582(10), Ingenta.
  11. Iterative refinement of the singular-value decomposition solution to the regression equations
    Henshall, J.M.; Smith, D.M.
    Computational Statistics & Data Analysis, v 22, n 6, Oct 23, 1996, p 573-582, Compendex.
  12. Sor-Secant Methods  
    Jose Mario Martinez
    SIAM Journal on Numerical Analysis, Vol. 31, No. 1. (Feb., 1994), pp. 217-226, Jstor.
  13. The Sigma-Sor Algorithm and the Optimal Strategy for the Utilization of the Sor Iterative Method  
    Zbigniew I. Woznicki
    Mathematics of Computation, Vol. 62, No. 206. (Apr., 1994), pp. 619-644, Jstor.  
  14. Iterative refinement for constrained and weighted linear least squares.
    Gulliksson, M.
    BIT 34 (1994), no. 2, 239--253, MathSciNet.  
  15. An efficient implementation of certain iterative refinement preconditioners.
    Petrova, S. I.
    Computing 52 (1994), no. 1, 51--63, MathSciNet.  
  16. On iterative refinement for the spectral decomposition of symmetric matrices.
    Malyshev, Alexander N.
    East-West J. Numer. Math. 1 (1993), no. 1, 27--50, MathSciNet.  
  17. Parallel domain decomposition and iterative refinement algorithms.
    Bjørstad, Petter E.; Moe, Randi; Skogen, Morten
    Parallel algorithms for partial differential equations (Kiel, 1990), 28--46,
    Notes Numer. Fluid Mech., 31, Vieweg, Braunschweig, 1991, MathSciNet.  
  18. Iterative refinement of a solution of systems of linear equations. (Russian)
    Kirilyuk, O. P.
    Trudy Inst. Mat. (Novosibirsk) 17 (1990), Vychisl. Metody Linein. Algebry, 5--18, MathSciNet.  
  19. Iterative refinement and reliable computing.
    Björck, Åke
    Reliable numerical computation, 249--266, Oxford Sci. Publ., Oxford Univ. Press, New York, 1990, MathSciNet.  
  20. Optimal iterative refinement methods, in Domain Decomposition Methods  
    O. B. Wildlund  
    Society for Industrial and Applied Mathematics, Philadelphia, 1989.
  21. Optimal iterative refinement methods.
    Widlund, Olof B.
    Domain decomposition methods (Los Angeles, CA, 1988), 114--125, SIAM, Philadelphia, PA, 1989, MathSciNet.  
  22. Use of Iterative Refinement in the Solution of Sparse Linear Systems  
    Zahari Zlatev  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 2. (Apr., 1982), pp. 381-399, Jstor.  
  23. Iterative refinement of approximations to a generalized inverse of a matrix.
    Mönch, W.
    Computing 28 (1982), no. 1, 79--87, MathSciNet.  
  24. Iterative refinement for linear systems in variable-precision arithmetic.
    Kielbasi'nski, Andrzej
    BIT 21 (1981), no. 1, 97--103, MathSciNet.  
  25. On an Accelerated Overrelaxation Iterative Method for Linear Systems With Strictly Diagonally Dominant Matrix  
    M. Madalena Martins  
    Mathematics of Computation > Vol. 35, No. 152 (Oct., 1980), pp. 1269-1273, Jstor.      
  26. Iterative Refinement Implies Numerical Stability for Gaussian Elimination  
    Robert D. Skeel  
    Mathematics of Computation, Vol. 35, No. 151. (Jul., 1980), pp. 817-832, Jstor.  
  27. Implementation Of An Iterative Refinement Option In A Code For Large And Sparse Systems  
    Zlatev, Zahari; Schaumburg, Kjeld; Wasniewski, Jerzy
    Computers & Chemistry, v 4, n 2, 1980, p 87-99, Compendex.
  28. Solutions To Weighted Least Squares Problems By Modified Gram-Schmidt With Iterative Refinement  
    Wampler, Roy H.  
    ACM Transactions on Mathematical Software, v 5, n 4, Dec, 1979, p 457-465, Compendex.
  29. Comment on the Iterative Refinement of Least-Squares Solutions
    Ake Bjorck
    Journal of the American Statistical Association > Vol. 73, No. 361 (Mar., 1978), pp. 161-166, Jstor.   
  30. An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix  
    J. A. Meijerink; H. A. van der Vorst  
    Mathematics of Computation > Vol. 31, No. 137 (Jan., 1977), pp. 148-162, Jstor.       
  31. Convergent Powers of a Matrix with Applications to Iterative Methods for Singular Linear Systems  
    Carl D. Meyer, Jr.; R. J. Plemmons  
    SIAM Journal on Numerical Analysis > Vol. 14, No. 4 (Sep., 1977), pp. 699-705, Jstor.    
  32. Iterative refinement implies numerical stability.
    Jankowski, M.; Wozniakowski, H.
    Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 3, 303--311, MathSciNet.  
  33. Existence Criteria for Partial Matrix Factorizations in Iterative Methods  
    Robert Beauwens; Lena Quenon  
    SIAM Journal on Numerical Analysis > Vol. 13, No. 4 (Sep., 1976), pp. 615-643, Jstor.   
  34. On the Iterative Refinement of Least Squares Solutions  
    R. H. Fletcher   
    Journal of the American Statistical Association > Vol. 70, No. 349 (Mar., 1975), pp. 109-112, Jstor   
  35. On Iterative Refinement Of Triangular Linear Algebraic Systems  
    Tsao, Nai-Kuan
    Journal of the Franklin Institute, v 299, n 6, Jun, 1975, p 409-416, Compendex.
  36. A Generalization of the Additive Correction Methods for the Iterative Solution of Matrix Equations  
    A. Settari; K. Aziz  
    SIAM Journal on Numerical Analysis > Vol. 10, No. 3 (Jun., 1973), pp. 506-521, Jstor.       
  37. Monotone Convergence of the Sor-Newton Iterative Technique  
    Charles W. Schelin
    SIAM Journal on Numerical Analysis, Vol. 10, No. 5. (Oct., 1973), pp. 933-938, Jstor.  
  38. Iterative Refinement in Floating Point  
    Cleve B. Moler
    Source     Journal of the ACM, Volume 14 ,  Issue 2  (April 1967), Pages: 316 - 321.  
  39. Iterative Methods for Solving Matrix Equations  
    R. S. Varga
    American Mathematical Monthly, Vol. 72, No. 2, Part 2: Computers and Computing. (Feb.,1965), pp. 67-74, Jstor.  
  40. An Iterative Method for Computing the Generalized Inverse of an Arbitrary Matrix  
    Adi Ben-Israel  
    Mathematics of Computation > Vol. 19, No. 91 (Jul., 1965), pp. 452-455, Jstor.     
  41. On Over and Under Relaxation in the Theory of the Cyclic Single Step Iteration  
    A. Ostrowski
    Mathematical Tables and Other Aids to Computation, Vol. 7, No. 43. (Jul., 1953), pp. 152-159, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005