Bibliography for Pivoting Methods

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  1. Solving unsymmetric sparse systems of linearequations with PARDISO  
    Olaf Schenk;  Klaus Gärtner
    Future Generation Computer Systems 20 (2004) 475--487
  2. Probabilistic analysis of complex Gaussian elimination without pivoting
    Yeung, Man-Chung  
    Linear Algebra and Its Applications, v 384, n 1-3 SUPPL., Jun 1, 2004, p 109-134, Compendex.
  3. Scaled pivots and scaled partial pivoting strategies   
    Peña, Juan M.  
    SIAM Journal on Numerical Analysis, v 41, n 3, 2003, p 1022-1031, Compendex.
  4. Roundoff Error Estimates of the Modified Gram--Schmidt Algorithm with Column Pivoting
    Wei M.; Liu Q.
    Bit Numerical Mathematics, September 2003, vol. 43, no. 3, pp. 627-645(19), Ingenta.  
  5. Some Features of Gaussian Elimination with Rook Pivoting
    Chang X-W.
    Bit Numerical Mathematics, 2002, vol. 42, no. 1, pp. 66-83(18), Ingenta.  
  6. A robust ILU with pivoting based on monitoring the growth of the inverse factors
    Bollhofer M.
    Linear Algebra and its Applications, 15 November 2001, vol. 338, no. 1, pp. 201-218(18), Ingenta.  
  7. New pivoted banded linear equations solvers
    Stabrowski, M.M.  
    Communications in Numerical Methods in Engineering, v 16, n 5, May, 2000, p 315-323, Compendex.
  8. On the Robustness of Gaussian Elimination with Partial Pivoting
    Favati P.; Leoncini M.; Martinez A.
    Bit Numerical Mathematics, 2000, vol. 40, no. 1, pp. 62-73(12), Ingenta.  
  9. The Rook's pivoting strategy
    Poole, George; Neal, Larry
    Journal of Computational and Applied Mathematics, 1 November 2000, vol. 123, no. 1, pp. 353-369(17), Ingenta.  
  10. A supernodal approach to sparse partial pivoting.    
    Demmel, James W.; Eisenstat, Stanley C.; Gilbert, John R.; Li, Xiaoye S.; Liu, Joseph W. H.    
    SIAM J. Matrix Anal. Appl. 20 (1999), no. 3, 720--755 (electronic), MathSciNet.  
  11. Pivoting strategies leading to diagonal dominance by rows.    
    Peña, J. M.    
    Numer. Math. 81 (1998), no. 2, 293--304, MathSciNet.  
  12. Locality of reference in LU decomposition with partial pivoting.    
    Toledo, Sivan    
    SIAM J. Matrix Anal. Appl. 18 (1997), no. 4, 1065--1081, MathSciNet.  
  13. Probabilistic analysis of Gaussian elimination without pivoting.    
    Yeung, Man-Chung; Chan, Tony F.    
    SIAM J. Matrix Anal. Appl. 18 (1997), no. 2, 499--517, MathSciNet.  
  14. A new pivoting strategy for Gaussian elimination     
    Olschowka, Markus; Neumaier, Arnold    
    Linear Algebra Appl. 240 (1996), 131--151, MathSciNet.  
  15. Pivoting strategies leading to small bounds of the errors for certain linear systems.    
    Peña, J. M.    
    IMA J. Numer. Anal. 16 (1996), no. 2, 141--153, MathSciNet.  
  16. Fast Gaussian Elimination with Partial Pivoting for Matrices with Displacement Structure  
    I. Gohbert, T. Kailath, V. Olshevsky  
    Mathematics of Computation, Vol. 64, No. 212. (Oct., 1995), pp. 1557-1576, Jstor.  
  17. Fast Gaussian elimination with partial pivoting for matrices with displacement structure.    
    Gohberg, I.; Kailath, T.; Olshevsky, V.    
    Math. Comp. 64 (1995), no. 212, 1557--1576, MathSciNet.  
  18. A Comparison of Block Pivoting and Interior-Point Algorithms for Linear Least Squares Problems with Nonnegative Variables  
    Luis F. Portugal, Joaquim J. Judice, Luis N. Vicente  
    Mathematics of Computation, Vol. 63, No. 208. (Oct., 1994), pp. 625-643, Jstor.  
  19. Gaussian elimination with partial pivoting can fail in practice.    
    Foster, Leslie V.    
    SIAM J. Matrix Anal. Appl. 15 (1994), no. 4, 1354--1362, MathSciNet.  
  20. Pivoting to normalize a basic matrix
    Eaves, B. Curtis  
    Mathematical Programming, Series A, v 62, n 3-8, Dec, 1993, p 553-556, Compendex.  
  21. Processor arrays for matrix triangularisation with partial pivoting
    Wyrzykowski, R.  
    IEE Proceedings, Part E: Computers and Digital Techniques, v 139, n 2, Mar, 1992, p 165-169, Compendex.
  22. The role of pivoting in proving some fundamental theorems of linear algebra.    
    Klafszky, Emil; Terlaky, Tamás    
    Linear Algebra Appl. 151 (1991), 97--118, MathSciNet.  
  23. The principal pivoting method revisited.    
    Cottle, Richard W.    
    Math. Programming 48 (1990), no. 3, (Ser. B), 369--385, MathSciNet.  
  24. Gaussian elimination with pivoting on hypercubes
    Rivera, F.F.; Doallo, R.; Bruguera, J.D.; Zapata, E.L.; Peskin, R.
    Parallel Computing, v 14, n 1, May, 1990, p 51-60, Compendex.
  25. Block QR factorization algorithm using restricted pivoting
    Bischof, Christian H.  
    Proc Supercomput 89, 1989, p 248-256, Compendex.
  26. Regular processor arrays for matrix algorithms with pivoting.
    Roychowdhury, V.P.; Kailath, T.
    Proc Int Conf on Systolic Arrays, 1988, p 237-246, Compendex.
  27. Symbolic factorization for sparse Gaussian elimination with partial pivoting     
    George, Alan; Ng, Esmond    
    SIAM J. Sci. Statist. Comput. 8 (1987), no. 6, 877--898, MathSciNet.   
  28. Studie zur Pivotisierung beim Gaußschen Algorithmus. (German) [Study of pivoting in the Gauss algorithm] Rostock.    
    Berg, Lothar    
    Math. Kolloq. No. 30 (1986), 105--112, MathSciNet.  
  29. Analysis of pairwise pivoting in Gaussian elimination     
    Sorensen, Danny C.    
    IEEE Trans. Comput. 34 (1985), no. 3, 274--278, MathSciNet.  
  30. Partial pivoting strategies for symmetric Gaussian elimination.    
    Dax, Achiya    
    Math. Programming 22 (1982), no. 3, 288--303, MathSciNet.  
  31. Effect of Equilibration on Residual Size for Partial Pivoting  
    Robert D. Skeel  
    SIAM Journal on Numerical Analysis > Vol. 18, No. 3 (Jun., 1981), pp. 449-454, Jstor.   
  32. LU decomposition of M-matrices by elimination without pivoting.    
    Funderlic, R. E.; Plemmons, R. J.    
    Linear Algebra Appl. 41 (1981), 99--110, MathSciNet.  
  33. On Factoring a Class of Complex Symmetric Matrices Without Pivoting  
    Steven M. Serbin  
    Mathematics of Computation, Vol. 35, No. 152. (Oct., 1980), pp. 1231-1234, Jstor.  
  34. Algorithm 533 Em Dash Nspiv, A Fortran Subroutine For Sparse Gaussian Elimination With Partial Pivoting
    Sherman, Andrew H.
    ACM Transactions on Mathematical Software, v 4, n 4, Dec, 1978, p 391-398, Compendex.
  35. A note on partial pivoting and Gaussian elimination.    
    van Veldhuizen, M.    
    Numer. Math. 29 (1977/78), no. 1, 1--10, MathSciNet.  
  36. Hierarchical partition---a new optimal pivoting algorithm.    
    Lin, T. D.; Mah, R. S. H.    
    Math. Programming 12 (1977), no. 2, 260--278, MathSciNet.  
  37. Some New Results On Decomposition And Pivoting Of Large Sparse Systems Of Linear Equations.
    Jess, Jochen A. G.
    IEEE Transactions on Circuits and Systems, v CAS-23, n 12, Dec, 1976, p 729-738, Compendex.
  38. A Simple Proof for Partial Pivoting (in Mathematical Notes)  
    Donald J. Rose  
    American Mathematical Monthly, Vol. 82, No. 9. (Nov., 1975), pp. 919-921, Jstor.  
  39. Parallel Processing Algorithm For Matrix Pivoting
    Ho, C. W.; Zein, D. A.
    IBM Technical Disclosure Bulletin, v 18, n 8, Dec, 1975, p 2368-2371, Compendex.
  40. Partial Pivoting Strategies for Symmetric Matrices  
    James R. Bunch  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 3. (Jun., 1974), pp. 521-528, Jstor.  
  41. An optimal pivoting order for the solution of sparse systems of equations.    
    Nakhla, M.; Singhal, K.; Vlach, J.    
    IEEE Transactions on Circuits and Systems, v CAS-21, n 2, Mar, 1974, p 222-225, MathSciNet.  
  42. Probabilistic Approach To Optimal Pivoting And Prediction Of Fill-In For Random Sparse Matrices.
    Hsieh, Hsueh Y.; Ghausi, Mohammed S.
    IEEE Transactions on Circuit Theory, v CT-19, n 4, Jul, 1972, p 329-336, Compendex.
  43. On optimal-pivoting algorithms in sparse matrices.
    Hsieh, H. Y.; Ghausi, M. S.    
    IEEE Trans. Circuit Theory CT-19 (Jan, 1972), 93--96, MathSciNet.  
  44. Analysis of the Diagonal Pivoting Method  
    J. R. Bunch  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 4. (Dec., 1971), pp. 656-680, Jstor.  
  45. Maximum-Rank Minimum- Term- Rank Theorem For The Pivotal Transforms Of A Matrix
    IRI M
    Linear Algebra & Its Applications, v 2, n 4, Oct, 1969, p 427-46, Compendex.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005