Bibliography for LU Factorization

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  1. A new approach to backward error analysis LU factorization  
    Peña, J. M. A note on a paper by P. Amodio and F. Mazzia  
    [BIT 39 (1999), no. 3, 385--402; MR 2000e:65034]. BIT 41 (2001), no. 3, 640--643, MathSciNet.  
  2. On the block implicit LU algorithm for linear systems of equations.  
    Bodon, Elena  
    Math. Notes (Miskolc) 2 (2001), no. 1, 11--29, MathSciNet.  
  3. A grid-based multilevel incomplete LU factorization preconditioning technique for general sparse matrices.  
    Zhang, Jun  
    Appl. Math. Comput. 124 (2001), no. 1, 95--115, MathSciNet.  
  4. An incomplete LU-factorization algorithm based on block bordering.  
    Kolotilina, L. Yu.; Nikishin, A. A.; Yeremin, A. Yu.  
    Preconditioning techniques for large sparse matrix problems in industrial applications (Minneapolis, MN, 1999).
    Numer. Linear Algebra Appl. 7 (2000), no. 7-8, 543--567, MathSciNet.  
  5. S+  efficient 2D sparse LU factorization on parallel machines.  
    Shen, Kai; Yang, Tao; Jiao, Xiangmin  
    SIAM J. Matrix Anal. Appl. 22 (2000), no. 1, 282--305 (electronic), MathSciNet.  
  6. Some conditions for existence and stability of relaxed incomplete LU factorizations.  
    Gu, Gui-Ding  
    Appl. Numer. Math. 38 (2001), no. 1-2, 105--121, MathSciNet.  
  7. A multilevel dual reordering strategy for robust incomplete LU factorization of indefinite matrices.  
    Zhang, Jun  
    SIAM J. Matrix Anal. Appl. 22 (2000), no. 3, 925--947 (electronic), MathSciNet.  
  8. Efficient sparse LU factorization with left-right looking strategy on shared memory multiprocessors.  
    Schenk, O.; Gärtner, K.; Fichtner, W.  
    BIT 40 (2000), no. 1, 158--176, MathSciNet.  
  9. A new approach to backward error analysis of LU factorization.  
    Amodio, P.; Mazzia, F.  
    BIT 39 (1999), no. 3, 385--402, MathSciNet.  
  10. High-performance out-of-core sparse LU factorization.  
    Gilbert, John R.; Toledo, Sivan  
    Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing 1999 (San Antonio, TX), 10 pp., SIAM, Philadelphia, PA, 1999, MathSciNet.  
  11. On the sensitivity of the LU factorization.  
    Chang, Xiao-Wen; Paige, Christopher C.  
    BIT 38 (1998), no. 3, 486--501, MathSciNet.  
  12. Block LU factorizations of M-matrices.  
    McDonald, J. J.; Schneider, H.  
    Numer. Math. 80 (1998), no. 1, 109--130, MathSciNet.  
  13. Locality of reference in LU decomposition with partial pivoting.  
    Toledo, Sivan  
    SIAM J. Matrix Anal. Appl. 18 (1997), no. 4, 1065--1081, MathSciNet.  
  14. A remark on the inverse of principal matrices by implicit LU factorization.  
    Huang, Kaibin; Wu, Hebin  
    J. Math. Res. Exposition 17 (1997), no. 4, 527--528, MathSciNet.  
  15. Efficient parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes.  
    Liu, Zhiyong; Cheung, D. W.  
    Comput. Math. Appl. 33 (1997), no. 8, 39--50, MathSciNet.  
  16. On bounds for LU-factorizations of sparse matrices and their applications to incomplete factorization methods. (Russian)  
    Blatov, I. A.  
    Zh. Vychisl. Mat. Mat. Fiz. 37 (1997), no. 3, 259--276; translation in Comput. Math. Math. Phys. 37 (1997), no. 3, 255--273, MathSciNet.  
  17. Relative-error bounds for the LU decomposition via the GTH algorithm.  
    O'Cinneide, Colm Art  
    Numer. Math. 73 (1996), no. 4, 507--519, MathSciNet.  
  18. A necessary and sufficient condition for M-matrices and its relation to block LU factorization.  
    Yip, E. L.  
    Linear Algebra Appl. 235 (1996), 261--274, MathSciNet.  
  19. On the stability of the incomplete LU-factorizations and characterizations of H-matrices.  
    Messaoudi, A.  
    Numer. Math. 69 (1995), no. 3, 321--331, MathSciNet.  
  20. Stability of block LU factorization.  
    Demmel, James W.; Higham, Nicholas J.; Schreiber, Robert S.  
    Numer. Linear Algebra Appl. 2 (1995), no. 2, 173--190, MathSciNet.  
  21. Sign determinancy in LU factorization of P-matrices.  
    Johnson, Charles R.; Olesky, D. Dale; van den Driessche, P.  
    Proceedings of a Conference on Graphs and Matrices in honor of John Maybee (Boulder, CO, 1993). Linear Algebra Appl. 217 (1995), 155--166, MathSciNet.  
  22. Gaussian Elimination in Integer Arithmetic: An Application of the L-U Factorization   
    Thomas Hern     
    College Math Journal: Volume 24, Number 1, (1993), Pages: 67-70, 1993.  
  23. On the perturbation of LU, Cholesky, and QR factorizations.  
    Stewart, G. W.  
    SIAM J. Matrix Anal. Appl. 14 (1993), no. 4, 1141--1145, MathSciNet.  
  24. Recurrent neural networks for LU decomposition and Cholesky factorization.  
    Wang, J.; Wu, G.  
    Math. Comput. Modelling 18 (1993), no. 6, 1--8, MathSciNet.  
  25. Elimination structures for unsymmetric sparse LU factors.  
    Gilbert, John R.; Liu, Joseph W. H.  
    SIAM J. Matrix Anal. Appl. 14 (1993), no. 2, 334--352, MathSciNet.  
  26. Construction of LU Factors of the Basis to Reduce Build-Up during Simplex Iterations  
    Bob Hattersley, Lynne Mackley  
    The Journal of the Operational Research Society, Vol. 43, No. 5, Mathematical Programming in Honour of Ailsa Land. (May, 1992), pp. 507-518, Jstor.  
  27. Backward error analysis of LU-decomposition for pentadiagonal matrices.  
    Yalamov, P. Y.  
    Serdica 18 (1992), no. 3-4, 215--223, MathSciNet.  
  28. Stable algorithm for updating dense LU factorization after row or column exchange and row and column addition or deletion.  
    Gondzio, J.  
    Optimization 23 (1992), no. 1, 7--26, MathSciNet.  
  29. On LU decomposition of a centrosymmetric matrix.  
    Ramabhadrasarma, Ivatury; Dattatreya Rao, A. V.; Venkata Ramana, K.  
    Inform. Sci. 63 (1992), no. 1-2, 3--10, MathSciNet.  
  30. Methods for the LU decomposition of sparse matrices in large-scale optimization systems: directions and prospects of development. (Russian)  
    Yadykin, A. B.; Tverskoui, I. V.  
    Voprosy Kibernet. (Moscow) No. 156 (1991), 111--152, MathSciNet.  
  31. On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization.  
    Hegland, Markus  
    Numer. Math. 59 (1991), no. 5, 453--472, MathSciNet.  
  32. Two-processor system for LU factorization of five-diagonal matrix.  
    Milovanovi'c, E. I.; Stojv cev, M. K.; Milovanovi'c, I. v Z.  
    Internat. J. Electron. 70 (1991), no. 1, 11--22, MathSciNet.  
  33. Elementary Row Operations and LU Decomposition  
    David Kraines, Vivian Kraines, David Smith  
    College Math Journal: Volume 21, Number 5, (1990), Pages: 418-419.   
  34. On the Stability of Relaxed Incomplete LU Factorizations  
    A. M. Bruaset, A. Tveito, R. Winther  
    Mathematics of Computation, Vol. 54, No. 190. (Apr., 1990), pp. 701-719, Jstor.  
  35. The accuracy of a parallel LU decomposition algorithm.  
    Tsao, N. K.  
    Comput. Math. Appl. 20 (1990), no. 7, 25--30, MathSciNet.  
  36. A new modified Cholesky factorization.  
    Schnabel, Robert B.; Eskow, Elizabeth  
    SIAM J. Sci. Statist. Comput. 11 (1990), no. 6, 1136--1158, MathSciNet.  
  37. On the LU factorization of Hessenberg matrices.  
    Neuman, Charles P.  
    IEEE Trans. Systems Man Cybernet. 19 (1989), no. 1, 139--140, MathSciNet.  
  38. A note on the parallel Cholesky factorization of wide banded matrices.  
    Conroy, John M.  
    Parallel Comput. 10 (1989), no. 2, 239--246, MathSciNet.  
  39. Stable LU factorization of H-matrices.  
    Ahac, Alan A.; Buoni, John J.; Olesky, D. D.  
    Linear Algebra Appl. 99 (1988), 97--110, MathSciNet.  
  40. A parallel algorithm for the general LU factorization.  
    Kincaid, David R.; Oppe, Thomas C.  
    Comm. Appl. Numer. Methods 4 (1988), no. 3, 349--359, MathSciNet.  
  41. Fast Gauss-Doolittle matrix triangulation.  
    Williams, F. W.; Kennedy, D.  
    Comput. & Structures 28 (1988), no. 2, 143--148, MathSciNet.  
  42. Cholesky decomposition of the Hilbert matrix.   
    Hitotumatu, Sin  
    Japan J. Appl. Math. 5 (1988), no. 1, 135--144, MathSciNet.
  43. Compact structural representation of sparse Cholesky, QR and LU factors.  
    George, Alan; Liu, Joseph W. H.  
    Computing methods in applied sciences and engineering, VII (Versailles, 1985), 93--106, North-Holland, Amsterdam, 1986, MathSciNet.  
  44. LU-Factorization of Operators on l1  
    Kevin T. Andrews, Philip W. Smith, Joseph D. Ward  
    Proceedings of the American Mathematical Society, Vol. 98, No. 2. (Oct., 1986), pp. 247-252, Jstor.  
  45. A Stability Analysis of Incomplete LU Factorizations  
    Howard C. Elman  
    Mathematics of Computation, Vol. 47, No. 175. (Jul., 1986), pp. 191-217, Jstor.  
  46. LU-decompositions of tridiagonal irreducible H-matrices.  
    Harrod, W. J.  
    SIAM J. Algebraic Discrete Methods 7 (1986), no. 2, 180--187, MathSciNet.  
  47. A stable method for the LU factorization of M-matrices.  
    Ahac, Alan A.; Olesky, D. D.  
    SIAM J. Algebraic Discrete Methods 7 (1986), no. 3, 368--378, MathSciNet.  
  48. Modification of the LU factorization of square matrices after changing with a dyad. (Hungarian)  
    Bartalos, István  
    Alkalmaz. Mat. Lapok 11 (1985), no. 1-2, 157--165, MathSciNet.  
  49. LU factorization on parallel computers.  
    Neta, Beny; Tai, Heng Ming  
    Comput. Math. Appl. 11 (1985), no. 6, 573--579, MathSciNet.  
  50. On the Existence and Computation of LU-Factorizations with Small Pivots  
    Tony F. Chan  
    Mathematics of Computation, Vol. 42, No. 166. (Apr., 1984), pp. 535-547, Jstor.  
  51. The stability of LU-decompositions of block tridiagonal matrices.  
    Mattheij, R. M. M.  
    Bull. Austral. Math. Soc. 29 (1984), no. 2, 177--205, MathSciNet.  
  52. Refined Error Analyses of Cholesky Factorization  
    Jean Meinguet  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 6. (Dec., 1983), pp. 1243-1250, Jstor.  
  53. A fast approximate LU method for solving a system of linear equations with special five-diagonal matrix. (Chinese)  
    Gao, De Ying  
    Numer. Math. J. Chinese Univ. 5 (1983), no. 1, 19--29, MathSciNet.  
  54. Elementary matrices and Crout reduction.  
    Rizvi, S. A. H.; Singh, V. N.  
    J. Indian Acad. Math. 5 (1983), no. 1, 9--11, MathSciNet.  
  55. LU decompositions of generalized diagonally dominant matrices.  
    Funderlic, R. E.; Neumann, M.; Plemmons, R. J.  
    Numer. Math. 40 (1982), no. 1, 57--69, MathSciNet.  
  56. Implicit Schemes and LU Decompositions  
    A. Jameson, E. Turkel  
    Mathematics of Computation, Vol. 37, No. 156. (Oct., 1981), pp. 385-397, Jstor.  
  57. L decomposition of M-matrices by elimination without pivoting.  
    Funderlic, R. E.; Plemmons, R. J.  
    Linear Algebra Appl. 41 (1981), 99--110, MathSciNet.  
  58. The fast approximate LU method of the special tridiagonal linear simultaneous equations. (Chinese)  
    Gao, De Ying; Xu, Feng; Pai, Nai De  
    Math. Numer. Sinica 3 (1981), no. 1, 10--17, MathSciNet.  
  59. A Comment on Syminv: An Algorithm for the Inversion of a Positive Definite Matrix by the Cholesky Decomposition (in Computer Algorithm)  
    J. Stewart  
    Econometrica, Vol. 42, No. 4. (Jul., 1974), p. 771, Jstor.  
  60. A Geometric Theory for the QR, LU and Power Iterations  
    B. N. Parlett, W. G. Poole, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 2. (Apr., 1973), pp. 389-412., Jstor.  
  61. SYMINV: An Algorithm for the Inversion of a Positive Definite Matrix by the Cholesky Decomposition (in Computer Algorithms)  
    Terry Seaks  
    Econometrica, Vol. 40, No. 5. (Sep., 1972), pp. 961-962, Jstor.  
  62. The Crout reduction for sparse matrices.  
    Tewarson, R. P.  
    Comput. J. 12 1969/1970 158--159, MathSciNet.  
  63. The Doolittle method and the fitting of polynomials to weighted data   
    P. G. Guest  
    Biometrika, Vol. 40, No. 1/2. (Jun., 1953), pp. 229-231, Jstor.  
  64. Accuracy in the Doolittle solution  
    Dickson H. Leavens
    Econometrica, Vol. 15, No. 1. (Jan., 1947), pp. 45-50, Jstor.  
  65. Note on the Doolittle solution  
    Nancy Bruner  
    Econometrica, Vol. 15, No. 1. (Jan., 1947), pp. 43-44, Jstor.  
  66. Correlation concepts and the Doolittle method  
    Dudley J. Cowden
    Journal of the American Statistical Association, Vol. 38, No. 223. (Sep., 1943), pp. 327-334, Jstor.  
  67. The Doolittle Technique  
    Paul S. Dwyer  
    Annals of Mathematical Statistics, Vol. 12, No. 4. (Dec., 1941), pp. 449-458, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003