1. Enumeration of simple random walks and tridiagonal matrices.
   Cicuta, G. M.; Contedini, M.; Molinari, L.
   J. Phys. A 35 (2002), no. 5, 1125--1146
2. Extension of the Thomas algorithm to a class of algebraic linear equation systems involving quasi-block-tridiagonal matrices with isolated block-pentadiagonal rows, assuming variable block dimensions.
   Bieniasz, L. K.
   Computing 67 (2001), no. 4, 269--285, MathSciNet.  
3. Generalized scans and tridiagonal systems.
   Fischer, Paul F.; Preparata, Franco P.; Savage, John E.
   Theoret. Comput. Sci. 255 (2001), no. 1-2, 423--436, MathSciNet.  
4. The inverse of a tridiagonal matrix.
   Mallik, Ranjan K.
   Linear Algebra Appl. 325 (2001), no. 1-3, 109--139, MathSciNet.  
5. Some improvements for two-sided bounds on the inverse of diagonally dominant tridiagonal matrices.
   Peluso, R.; Politi, T.
   Linear Algebra Appl. 330 (2001), no. 1-3, 1--14, MathSciNet.  
6. A parallel method for linear equations with tridiagonal Toeplitz coefficient matrices.
   Garey, L. E.; Shaw, R. E.
   Comput. Math. Appl. 42 (2001), no. 1-2, 1--11, MathSciNet.  
7. Explicit inverses of some tridiagonal matrices.
   da Fonseca, C. M.; Petronilho, J.
   Linear Algebra Appl. 325 (2001), no. 1-3, 7--21, MathSciNet.  
8. Unicity of minimal rank completions for tri-diagonal partial block matrices.
   Bostian, A. A.; Woerdeman, H. J.
   Linear Algebra Appl. 325 (2001), no. 1-3, 23--55, MathSciNet.  
9. Reliable solution of tridiagonal systems of linear equations.
   Bar-On, Ilan; Leoncini, Mauro
   SIAM J. Numer. Anal. 38 (2000), no. 4, 1134--1153 (electronic), MathSciNet.  
10. A split-correct parallel algorithm for solving tridiagonal symmetric Toeplitz systems.
    McNally, J. M.; Garey, L. E.; Shaw, R. E.
    Int. J. Comput. Math. 75 (2000), no. 3, 303--313, MathSciNet.  
11. A parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension.
    Rossi, Tuomo; Toivanen, Jari
    SIAM J. Sci. Comput. 20 (1999), no. 5, 1778--1796 (electronic), MathSciNet.  
12. Stable solution of tridiagonal systems.
    Bar-On, Ilan; Leoncini, Mauro
    Numer. Algorithms 18 (1998), no. 3-4, 361--388, MathSciNet.  
13. Reliable computation of the condition number of a tridiagonal matrix in O(n) time.
    Dhillon, Inderjit S.
    SIAM J. Matrix Anal. Appl. 19 (1998), no. 3, 776--796 (electronic), MathSciNet.  
14. The use of the factorization of five-diagonal matrices by tridiagonal Toeplitz matrices.
    Diele, F.; Lopez, L.
    Appl. Math. Lett. 11 (1998), no. 3, 61--69, MathSciNet.  
15. A parallel solver for circulant Toeplitz tridiagonal systems on hypercubes.
    Wu, Jung-Gen; Yan, Wen-Ming; Chung, Kuo-Liang
    J. Sci. Comput. 12 (1997), no. 4, 409--431, MathSciNet.  
16. The parallel solution of tridiagonal systems by recursive striding.
    Evans, D. J.
    Parallel Algorithms Appl. 10 (1997), no. 3-4, 161--164, MathSciNet.  
17. A fast parallel Cholesky decomposition algorithm for tridiagonal symmetric matrices.
    Bar-On, Ilan; Codenotti, Bruno; Leoncini, Mauro
    SIAM J. Matrix Anal. Appl. 18 (1997), no. 2, 403--418, MathSciNet.  
18. Analytical inversion of general tridiagonal matrices.
    Huang, Y.; McColl, W. F.
    J. Phys. A 30 (1997), no. 22, 7919--7933, MathSciNet.  
19. Economic modification of a sweep's method for solution of tridiagonal linear algebraic system of equation.
    Zarnan, J. A.
    Math. Balkanica (N.S.) 10 (1996), no. 2-3, 203--210, MathSciNet.  
20. Vectorized algorithms for solving special tridiagonal systems.
    Chung, Kuo-Liang; Yan, Wen-Ming
    Comput. Math. Appl. 32 (1996), no. 12, 1--14, MathSciNet.  
21. Analytical inversion of symmetric tridiagonal matrices.
    Hu, G. Y.; O'Connell, R. F.
    J. Phys. A 29 (1996), no. 7, 1511--1513, MathSciNet.  
22. Generalized scans and tri-diagonal systems.
    Fischer, Paul F.; Preparata, Franco P.; Savage, John E.
    STACS 95 (Munich, 1995), 168--180, Lecture Notes in Comput. Sci., 900, Springer, Berlin, 1995, MathSciNet.  
23. On the algebraic construction of tri-diagonal matrices with given characteristic polynomial.
    Williamson, Clifton J.
    Number theory (Halifax, NS, 1994), 417--431, CMS Conf. Proc., 15, Amer. Math. Soc., Providence, RI, 1995, MathSciNet.  
24. Backward Error Analysis of Cyclic Reduction for the Solution of Tridiagonal Systems  
    Pierluigi Amodio, Francesca Mazzia  
    Mathematics of Computation, Vol. 62, No. 206. (Apr., 1994), pp. 601-617, Jstor.  
25. Tridiagonal matrices.
    Newman, Morris
    Linear Algebra Appl. 201 (1994), 51--55, MathSciNet.  
26. Bounds for the solutions of a class of tridiagonal linear systems.
    Lopez, L.
    Linear Algebra Appl. 202 (1994), 221--233, MathSciNet.  
27. An error model for Swarztrauber's parallel tridiagonal equation solver.
    Tsao, Nai Kuan
    SIAM J. Matrix Anal. Appl. 15 (1994), no. 2, 692--713, MathSciNet.  
28. Parallel Factorizations for Tridiagonal Matrices  
    P. Amodio, L. Brugnano, T. Politi  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 3. (Jun., 1993), pp. 813-823, Jstor.  
29. The parallel strides reduction algorithms for solving tridiagonal linear systems.
    Evans, D. J.; Yousif, W. S.
    Neural Parallel Sci. Comput. 1 (1993), no. 1, 29--42, MathSciNet.  
30. Wavefronts for a cooperative tridiagonal system of differential equations.
    Hankerson, D.; Zinner, B.
    J. Dynam. Differential Equations 5 (1993), no. 2, 359--373, MathSciNet.  
31. The invertibility of a class of tridiagonal matrices.
    Lopez, L.
    Appl. Math. Lett. 5 (1992), no. 4, 47--51, MathSciNet.  
32. An accurate tridiagonal equation solver.
    Tsao, Nai Kuan
    Inform. Sci. 64 (1992), no. 1-2, 27--33, MathSciNet.  
33. Efficient tridiagonal solvers on multicomputers.
    Sun, Xian-He; Zhang, Hong; Ni, Lionel M.
    IEEE Trans. Comput. 41 (1992), no. 3, 286--296, MathSciNet.  
34. A tricyclic tridiagonal equation solver.
    Dodson, David S.; Levin, Stewart A.
    SIAM J. Matrix Anal. Appl. 13 (1992), no. 4, 1246--1254, MathSciNet.  
35. Parallel factorizations and parallel solvers for tridiagonal linear systems.
    Amodio, P.; Brugnano, L.
    Second NIU Conference on Linear Algebra, Numerical Linear Algebra and Applications (DeKalb, IL, 1991). Linear Algebra Appl. 172 (1992), 347--364, MathSciNet.  
36. Cyclic Reduction for Tridiagonal Systems of Equations with Interval Coefficients on Vector Computers  
    Hartmut Schwandt  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 3. (Jun., 1989), pp. 661-680, Jstor.  
37. An estimate for tri-diagonal matrices. (Russian)
    Sander, S. A.
    Sibirsk. Mat. Zh. 30 (1989), no. 4, 171--173, 218; translation in Siberian Math. J. 30 (1989), no. 4, 635--636 (1990), MathSciNet.  
38. Parallel methods for tridiagonal equations.
    Kaur, D.; Wallach, Y.
    Computing 40 (1988), no. 3, 267--272, MathSciNet.  
39. Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tri-diagonal matrices.
    van Doorn, Erik A.
    J. Approx. Theory 51 (1987), no. 3, 254--266, MathSciNet.  
40. Analysis of a parallel solution method for tridiagonal linear systems.
    van der Vorst, Henk A.
    Parallel Comput. 5 (1987), no. 3, 303--311, MathSciNet.  
41. Explicit solution of block tridiagonal systems of linear equations.
    Evans, D. J.; Yousif, W. S.
    Inform. Process. Lett. 24 (1987), no. 3, 207--209, MathSciNet.  
42. An iterative algorithm for the solution of a tridiagonal linear system of equations.
    Yousif, W. S.; Evans, D. J.
    Comput. Math. Appl. Ser. A 12 (1986), no. 10, 1019--1027, MathSciNet.  
43. Efficient algorithms for computing the condition number of a tridiagonal matrix.
    Higham, Nicholas J.
    SIAM J. Sci. Statist. Comput. 7 (1986), no. 1, 150--165, MathSciNet.  
44. On the Solution of Block Tridiagonal Systems of Linear Algebraic Equations having a Special Structure  
    J. R. Cash  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 6. (Dec., 1982), pp. 1220-1232, Jstor.  
45. Inversion of tridiagonal matrices.
    Lewis, Jerry W.
    Numer. Math. 38 (1981/82), no. 3, 333--345, MathSciNet.  
46. Eigenvalues of a Tri-Diagonal Matrix: Problem 80-4 (in Solutions)  
    D. K. Ross  
    SIAM Review, Vol. 23, No. 1. (Jan., 1981), pp. 112-113, Jstor.  
47. On the Solution of Certain Toeplitz Tridiagonal Linear Systems  
    D. J. Evans  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 5. (Oct., 1980), pp. 675-680, Jstor.  
48. Eigenvalues of a Tri-diagonal Matrix: Problem 80-4 (in Problems)  
    D. K. Ross  
    SIAM Review, Vol. 22, No. 1. (Jan., 1980), p. 98, Jstor.  
49. A Parallel Algorithm for Solving General Tridiagonal Equations  
    Paul N. Swarztrauber  
    Mathematics of Computation, Vol. 33, No. 145. (Jan., 1979), pp. 185-199, Jstor.  
50. A sixth-order tridiagonal finite difference method for general non-linear two-point boundary value problems.
    Chawla, M. M.
    J. Inst. Math. Appl. 24 (1979), no. 1, 35--42, MathSciNet.  
51. A New Proof of Global Convergence for the Tridiagonal QL Algorithm  
    W. Hoffmann, B. N. Parlett  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 5. (Oct., 1978), pp. 929-937, Jstor.  
52. A Cyclic Reduction Algorithm for Solving Block Tridiagonal Systems of Arbitrary Dimension  
    Roland A. Sweet  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 4. (Sep., 1977), pp. 706-720, Jstor.  
53. Some Aspects of the Cyclic Reduction Algorithm for Block Tridiagonal Linear Systems  
    Don Heller  
    SIAM Journal on Numerical Analysis, Vol. 13, No. 4. (Sep., 1976), pp. 484-496, Jstor.  
54. Tridiagonal Fourth Order Approximations to General Two-Point Nonlinear Boundary Value Problems with Mixed Boundary Conditions  
    Robert S. Stepleman  
    Mathematics of Computation, Vol. 30, No. 133. (Jan., 1976), pp. 92-103, Jstor.  
55. Algorithms for the solution of cyclic tridiagonal systems.
    Temperton, Clive
    J. Computational Phys. 19 (1975), no. 3, 317--323, MathSciNet.  
56. A fast method for solving a class of tridiagonal linear systems.
    Malcolm, Michael A.; Palmer, John
    Comm. ACM 17 (1974), 14--17, MathSciNet.  
57. Methods for inverting tri-diagonal matrices. (Russian)
    Buhberger, B.; Emel\cprime janenko, G. A.
    Z. Vycisl. Mat. i Mat. Fiz. 13 (1973), 546--554, 810, MathSciNet.  
58. On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations
    J. M. Varah  
    Mathematics of Computation, Vol. 26, No. 120. (Oct., 1972), pp. 859-868, Jstor.  
59. A Noniterative Algorithm for Tridiagonal Transportation Problems and Its Generalization (in Programming)  
    Benjamin Lev  
    Operations Research, Vol. 20, No. 1. (Jan. - Feb., 1972), pp. 109-125, Jstor.  
60. A Stable, Rational QR Algorithm for the Computation of the Eigenvalues of an Hermitian, Tridiagonal Matrix  
    Christian H. Reinsch  
    Mathematics of Computation, Vol. 25, No. 115. (Jul., 1971), pp. 591-597, Jstor.  
61. Computation of determinants for certain tridiagonal matrices.
    Law, A. G.
    Matrix Tensor Quart. 21 (1971), 83--84, MathSciNet.  
62. The Explicit Inverse of a Tridiagonal Matrix  
    P. Schlegel  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), p. 665, Jstor.  
63. Inequalities on the Elements of the Inverse of a Certain Tridiagonal Matrix  
    D. Kershaw  
    Mathematics of Computation, Vol. 24, No. 109. (Jan., 1970), pp. 155-158, Jstor.  
64. Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems  
    Charlotte F. Fischer, Riaz A. Usmani  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 1. (Mar., 1969), pp. 127-142, Jstor.  
65. Extremal Properties of Balanced Tri-Diagonal Matrices (in Technical Notes and Short Papers)  
    Peter A. Businger  
    Mathematics of Computation, Vol. 23, No. 105. (Jan., 1969), pp. 193-195, Jstor.  
66. On the Computation of the Eigenvalues of a Tridiagonal Matrix (in Technical Notes and Short Papers)  
    I. Gargantini  
    Mathematics of Computation, Vol. 23, No. 106. (Apr., 1969), pp. 403-405, Jstor.  
67. An exclusion theorem for tri-diagonal matrices.
    Jayne, John W.
    Proc. Edinburgh Math. Soc. (2) 16 1968/1969 251--253, MathSciNet.  
68. An Application of Tridiagonal Matrices to Network Synthesis  
    R. Yarlagadda  
    SIAM Journal on Applied Mathematics, Vol. 16, No. 6. (Nov., 1968), pp. 1146-1162, Jstor.  
69. On the Reduction of an Arbitrary Real Square Matrix to Tridiagonal Form (in Technical Notes and Short Papers)  
    H. H. Wang, R. T. Gregory  
    Mathematics of Computation, Vol. 18, No. 87. (Jul., 1964), pp. 501-505, Jstor.  
70. Errata: Bounds for Eigenvalues of Certain Tridiagonal Matrices  
    Peter Henrici  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 2. (Jun., 1964), p. 497, Jstor.  
71. The Reduction of an Arbitrary Real Square Matrix to Tri-Diagonal Form Using Similarity Transformations (in Technical Notes and Short Papers)
    C. Donald La Budde
    Mathematics of Computation, Vol. 17, No. 84. (Oct., 1963), pp. 433-437, Jstor.  
72. Bounds for Eigenvalues of Certain Tridiagonal Matrices  
    Peter Henrici  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 2. (Jun., 1963), pp. 281-290, Jstor.  
73. Note on the solution of certain tri-diagonal systems of linear equations.
    Evans, D. J.; Forrington, C. V. D.
    Comput. J. 5 1962/1963 327--328, MathSciNet.  
74. Bounds for Eigenvalues of Tridiagonal Symmetric Matrices Computed by the LR Method  
    Gene H. Golub  
    Mathematics of Computation, Vol. 16, No. 80. (Oct., 1962), pp. 438-445, Jstor.  
75. On the choice of the best relaxation factor for the solution of systems of equations with a quasi-tri-diagonal matrix. (Russian)
    Birjukova, L. D.
    1963 Kazan State Univ. Sci. Survey Conf. 1962 (Russian) pp. 122--124 Izdat. Kazan. Univ., Kazan, MathSciNet.  
76. Instability of the elimination method of reducing a matrix to tri-diagonal form.
    Wilkinson, J. H.
    Comput. J. 5 1962 61--70, MathSciNet.  
77. Latent roots of tri-diagonal matrices.
    Arscott, F. M.
    Proc. Edinburgh Math. Soc. (2) 12 1960/1961 Edinburgh Math. Notes No. 44, 5--7, MathSciNet.  
78. On the Propagation of Errors in the Inversion of Certain Tridiagonal Matrices  
    Arnold N. Lowan  
    Mathematics of Computation, Vol. 14, No. 72. (Oct., 1960), pp. 333-338, Jstor.  
79. Sequential Reduction to Tridiagonal Form  
    F. L. Bauer  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 7, No. 1. (Mar., 1959), pp. 107-113, Jstor.  

(c) John H. Mathews 2003