1. Stability of a pivoting strategy for parallel Gaussian elimination.  
   Mead, J. L.; Renaut, R. A.; Welfert, B. D.  
   BIT 41 (2001), no. 3, 633--639, MathSciNet.  
2. Gaussian elimination for the solution of linear systems of equations.  
   Meurant, Gérard  
   Handbook of numerical analysis, Vol. VII, 3--170, Handb. Numer. Anal., VII, North-Holland, Amsterdam, 2000, MathSciNet.  
3. On the robustness of Gaussian elimination with partial pivoting.  
   Favati, Paola; Leoncini, Mauro; Martinez, Angeles  
   BIT 40 (2000), no. 1, 62--73, MathSciNet.  
4. Bounding the growth factor in Gaussian elimination for Buckley's class of complex symmetric matrices.  
   Ikramov, Khakim D.; Kucherov, Andrey B.  
   Numer. Linear Algebra Appl. 7 (2000), no. 5, 269--274, MathSciNet.  
5. Growth in Gaussian elimination for weighing matrices, W(n,n-1).  
   Koukouvinos, C.; Mitrouli, M.; Seberry, Jennifer  
   Linear Algebra Appl. 306 (2000), no. 1-3, 189--202, MathSciNet.  
6. Bulk-synchronous parallel Gaussian elimination.  
   Tiskin, A.  
   Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 258 (1999), Teor. Predst. Din. Sist. Komb. Algoritm. Metody. 4, 115--133, 356--357, MathSciNet.  
7. An asynchronous parallel supernodal algorithm for sparse Gaussian elimination.  
   Demmel, James W.; Gilbert, John R.; Li, Xiaoye S.  
   Sparse and structured matrices and their applications (Coeur d'Alene, ID, 1996). SIAM J. Matrix Anal. Appl. 20 (1999), no. 4, 915--952 (electronic), MathSciNet.  
8. Growth in Gaussian elimination, orthogonal matrices, and the 2-norm.  
   Barlow, Jesse L.; Zha, Hongyuan  
   SIAM J. Matrix Anal. Appl. 19 (1998), no. 3, 807--815 (electronic), MathSciNet.  
9. Symmetric Gaussian elimination for Cauchy-type matrices with application to positive definite Toeplitz matrices.  
   Huckle, Thomas  
   Numer. Math. 79 (1998), no. 2, 213--229, MathSciNet.  
10. Gaussian Elimination and Dynamical Systems  
    Kathie Yerion  
    College Math Journal: Volume 28, Number 2, (1997), Pages: 89-97.   
11. The triangular matrices of Gaussian elimination and related decompositions.  
    Stewart, G. W.  
    IMA J. Numer. Anal. 17 (1997), no. 1, 7--16, MathSciNet.  
12. On the parallel complexity of Gaussian elimination with pivoting.  
    Leoncini, M.  
    1994 ACM Symposium on Parallel Algorithms and Architectures (Cape May, NJ, 1994). J. Comput. System Sci. 53 (1996), no. 3, 380--394, MathSciNet.  
13. A new pivoting strategy for Gaussian elimination.  
    Olschowka, Markus; Neumaier, Arnold  
    Linear Algebra Appl. 240 (1996), 131--151, MathSciNet.  
14. Combining Interior-Point and Pivoting Algorithms for Linear Programming  
    Erling D. Andersen, Yinyu Ye  
    Management Science, Vol. 42, No. 12. (Dec., 1996), pp. 1719-1731, Jstor.  
15. 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.  
16. 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.  
17. A new Gaussian elimination-based algorithm for parallel solution of linear equations.  
    Balasubramanya Murthy, K. N.; Siva Ram Murthy, C.  
    Comput. Math. Appl. 29 (1995), no. 7, 39--54, MathSciNet.  
18. Gaussian elimination with partial pivoting can fail in practice.  
    Foster, Leslie V.  
    SIAM J. Matrix Anal. Appl. 15 (1994), no. 4, 1354--1362, MathSciNet.  
19. 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.       
20. A collection of problems for which Gaussian elimination with partial pivoting is unstable.  
    Wright, Stephen J.  
    SIAM J. Sci. Comput. 14 (1993), no. 1, 231--238, MathSciNet.  
21. Gaussian elimination: when is scaling beneficial?  
    Poole, George; Neal, Larry  
    Directions in matrix theory (Auburn, AL, 1990). Linear Algebra Appl. 162/164 (1992), 309--324, MathSciNet.  
22. Variations on the Theme of Gaussian Elimination  
    D. Kershaw  
    The Journal of the Operational Research Society, Vol. 43, No. 8, Mathematical Methods and Models in Honour of Steven Vajda. (Aug., 1992), pp. 821-827, Jstor.  
23. Gram-Schmidt Orthogonalization by Gauss Elimination (in The Teaching of Mathematics)  
    Lyle Pursell, S. Y. Trimble  
    American Mathematical Monthly, Vol. 98, No. 6. (Jun. - Jul., 1991), pp. 544-549, Jstor.  
24. Another Elementary Approach to the Jordan Form (in Notes)  
    J. I. Hall  
    American Mathematical Monthly, Vol. 98, No. 4. (Apr., 1991), pp. 336-340, Jstor.  
25. On growth in Gaussian elimination with complete pivoting.  
    Gould, Nick  
    SIAM J. Matrix Anal. Appl. 12 (1991), no. 2, 354--361, MathSciNet.  
26. Pivot estimation for Gaussian elimination. (Chinese)  
    Zhou, Rong Fu  
    Math. Appl. 3 (1990), no. 3, 52--59, MathSciNet.  
27. Bounding the error in Gaussian elimination for tridiagonal systems.  
    Higham, Nicholas J.  
    SIAM J. Matrix Anal. Appl. 11 (1990), no. 4, 521--530, MathSciNet.  
28. Parallel sparse Gaussian elimination with partial pivoting.  
    George, Alan; Ng, Esmond  
    Supercomputers and large-scale optimization: algorithms, software, applications (Minneapolis, MN, 1988).
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29. Gaussian elimination with pivoting on hypercubes.  
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    Parallel Comput.14 (1990),no.1,51--60, MathSciNet.  
30. Optimal algorithms for Gaussian elimination on an MIMD computer.  
    Marrakchi, Mounir; Robert, Yves  
    Parallel Comput. 12 (1989), no. 2, 183--194, MathSciNet.  
31. Large growth factors in Gaussian elimination with pivoting.  
    Higham, Nicholas J.; Higham, Desmond J.  
    SIAM J. Matrix Anal. Appl. 10 (1989), no. 2, 155--164, MathSciNet.  
32. Gaussian elimination with pivoting is rmP-complete.  
    Vavasis, Stephen A.  
    SIAM J. Discrete Math. 2 (1989), no. 3, 413--423, MathSciNet.  
33. Block Gaussian elimination on a hypercube vector multiprocessor.  
    Robert, Y.; Tourancheau, B.  
    Rev. Mat. Apl. 10 (1989), no.1, 49--69, MathSciNet.  
34. Independent set orderings for parallel matrix factorization by Gaussian elimination.  
    Leuze, Michael R.  
    Parallel Comput. 10 (1989), no. 2, 177--191, MathSciNet.  
35. Why Should We Pivot in Gaussian Elimination?  
    Edward Rozema  
    College Math Journal: Volume 19, Number 1, (1988), Pages: 63-72.  
36. Growth in Gaussian Elimination  
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    American Mathematical Monthly, Vol. 95, No. 6. (Jun. - Jul., 1988), pp. 489-513, Jstor.  
37. On parallel Gaussian elimination with pivoting. (Chinese)  
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    J. Numer. Methods Comput. Appl. 9 (1988), no. 4, 207--213, MathSciNet.  
38. A remark on perfect Gaussian elimination of symmetric matrices.  
    Andreae, Thomas  
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39. Gaussian elimination on message passing architecture.  
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40. Parallel Gaussian elimination on an MIMD computer.  
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41. The Jordan Canonical Form: An Old Proof  
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    American Mathematical Monthly, Vol. 94, No. 3. (Mar., 1987), pp. 257-267, Jstor.  
42. Gauss-Jordan Reduction: A Brief History  
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    American Mathematical Monthly, Vol. 94, No. 2. (Feb., 1987), pp. 130-142, Jstor.  
43. Parallel Gaussian elimination on an optically interconnected data flow computer.  
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44. Gaussian elimination with partial pivoting and load balancing on a multiprocessor.  
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45. An Elementary Approach to the Jordan Form of a Matrix (in Notes)  
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46. Gaussian elimination on hypercubes.  
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47. Forward error analysis of Gaussian elimination. II.  
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48. Forward error analysis of Gaussian elimination. I. Error and residual estimates.  
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49. Analysis of pairwise pivoting in Gaussian elimination.  
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50. An implementation of Gaussian elimination with partial pivoting for sparse systems.  
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51. Gaussian elimination in floating-point arithmetic.  
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52. Gaussian elimination for diagonally dominant matrices.  
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53. Duality relations connected with Gaussian elimination. (Russian)  
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54. An Algorithmic Derivation of the Jordan Canonical Form  
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55. A posteriori error bounds for Gaussian elimination.  
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56. A new implementation of sparse Gaussian elimination.  
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57. A sufficient condition to permit block Gaussian elimination. (Korean)  
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58. Full matrix techniques in sparse Gaussian elimination.  
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59. Algorithms and data structures for sparse symmetric Gaussian elimination.  
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60. Effect of Equilibration on Residual Size for Partial Pivoting  
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61. On Factoring a Class of Complex Symmetric Matrices Without Pivoting  
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    Mathematics of Computation, Vol. 35, No. 152. (Oct., 1980), pp. 1231-1234, Jstor.  
62. Iterative Refinement Implies Numerical Stability for Gaussian Elimination  
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63. On Some Pivotal Strategies in Gaussian Elimination by Sparse Technique  
    Zahari Zlatev  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 1. (Feb., 1980), pp. 18-30, Jstor.  
64. Rounding error in Gaussian elimination of tridiagonal linear systems.  
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65. On the Gaussian elimination method based on the diagonal maximal pivoting for a system of linear equations whose matrix is Hermitian positive definite or is dia. (Korean)  
    Ho, Song Chang  
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66. A note on perfect Gaussian elimination.  
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67. A note on partial pivoting and Gaussian elimination.  
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    Numer. Math. 29 (1977/78), no. 1, 1--10, MathSciNet.  
68. A Negative Result on Sparse Matrix Splitting and Gaussian Elimination  
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    SIAM Journal on Numerical Analysis, Vol. 13, No. 6. (Dec., 1976), pp. 846-853, Jstor.  
69. Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form  
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70. A Simple Proof for Partial Pivoting (in Mathematical Notes)  
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    American Mathematical Monthly, Vol. 82, No. 9. (Nov., 1975), pp. 919-921, Jstor.  
71. Modifying Pivot Elements in Gaussian Elimination  
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    Mathematics of Computation, Vol. 28, No. 126. (Apr., 1974), pp. 537-542, Jstor.  
72. On the Number of Nonzeros Added when Gaussian Elimination is Performed on Sparse Random Matrices  
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    Mathematics of Computation, Vol. 28, No. 125. (Jan., 1974), pp. 219-230, Jstor.  
73. Partial Pivoting Strategies for Symmetric Matrices  
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    SIAM Journal on Numerical Analysis, Vol. 11, No. 3. (Jun., 1974), pp. 521-528, Jstor.  
74. Analysis of the Diagonal Pivoting Method  
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    SIAM Journal on Numerical Analysis, Vol. 8, No. 4. (Dec., 1971), pp. 656-680, Jstor.  
75. The Generalized Jordan Canonical Form (in Classroom Notes)  
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    American Mathematical Monthly, Vol. 77, No. 4. (Apr., 1970), pp. 392-395, Jstor.  
76. A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination  
    Kenneth M. Brown  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 4. (Dec., 1969), pp. 560-569, Jstor.  
77. Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination  
    Erwin H. Bareiss  
    Mathematics of Computation, Vol. 22, No. 103. (Jul., 1968), pp. 565-578.
78. The Jordan Canonical Form of a Particular Matrix (in Mathematical Notes)  
    A. Arcese  
    American Mathematical Monthly, Vol. 75, No. 7. (Aug. - Sep., 1968), pp. 752-753, Jstor.  
79. A Principal Pivoting Simplex Algorithm for Linear and Quadratic Programming  
    Robert L. Graves  
    Operations Research, Vol. 15, No. 3. (May - Jun., 1967), pp. 482-494, Jstor.
80. Erratum: Diagonalization of Quadratic Forms by Gauss Elimination  
    Charles S. Beightler  
    Management Science, Vol. 12, No. 11, Series A, Sciences. (Jul., 1966), p. 908, Jstor.  
81. Diagonalization of Quadratic Forms by Gauss Elimination  
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    Management Science, Vol. 12, No. 5, Series A, Sciences. (Jan., 1966), pp. 371-379, Jstor.  
82. Gauss Elimination for Singular Matrices (in Technical Notes and Short Papers)  
    George Shapiro  
    Mathematics of Computation, Vol. 17, No. 84. (Oct., 1963), pp. 441-445, Jstor.  
83. An Elementary Development of the Jordan Canonical Form  
    S. Cater  
    American Mathematical Monthly, Vol. 69, No. 5. (May, 1962), pp. 391-393, Jstor.  
84. The Use of Linear Graphs in Gauss Elimination  
    S. Parter  
    SIAM Review, Vol. 3, No. 2. (Apr., 1961), pp. 119-130, Jstor.  
85. Some Elementary Properties of Ill Conditioned Matrices and Linear Equations  
    N. S. Mendelsohn  
    American Mathematical Monthly, Vol. 63, No. 5. (May, 1956), pp. 285-295, Jstor.  

(c) John H. Mathews 2003