Bibliography for Tri-Diagonal Matrices

short

  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. The inverse of a tridiagonal matrix.
    Mallik, Ranjan K.
    Linear Algebra Appl. 325 (2001), no. 1-3, 109--139, MathSciNet.  
  3. 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.  
  4. 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.  
  5. Analytical inversion of symmetric tridiagonal matrices.
    Hu, G. Y.; O'Connell, R. F.
    J. Phys. A 29 (1996), no. 7, 1511--1513, MathSciNet.  
  6. 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.  
  7. Tridiagonal matrices.
    Newman, Morris
    Linear Algebra Appl. 201 (1994), 51--55, MathSciNet.  
  8. 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.  
  9. Wavefronts for a cooperative tridiagonal system of differential equations.
    Hankerson, D.; Zinner, B.
    J. Dynam. Differential Equations 5 (1993), no. 2, 359--373, MathSciNet.  
  10. An accurate tridiagonal equation solver.
    Tsao, Nai Kuan
    Inform. Sci. 64 (1992), no. 1-2, 27--33, MathSciNet.  
  11. 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.  
  12. 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.  
  13. 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.  
  14. Inversion of tridiagonal matrices.
    Lewis, Jerry W.
    Numer. Math. 38 (1981/82), no. 3, 333--345, MathSciNet.  
  15. 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.  
  16. 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.  
  17. 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.  
  18. A Parallel Algorithm for Solving General Tridiagonal Equations  
    Paul N. Swarztrauber  
    Mathematics of Computation, Vol. 33, No. 145. (Jan., 1979), pp. 185-199, Jstor.  
  19. 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.  
  20. 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.  
  21. 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.  
  22. 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.  
  23. Algorithms for the solution of cyclic tridiagonal systems.
    Temperton, Clive
    J. Computational Phys. 19 (1975), no. 3, 317--323, MathSciNet.  
  24. A fast method for solving a class of tridiagonal linear systems.
    Malcolm, Michael A.; Palmer, John
    Comm. ACM 17 (1974), 14--17, MathSciNet.  
  25. 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.  
  26. 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.  
  27. 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.  
  28. Computation of determinants for certain tridiagonal matrices.
    Law, A. G.
    Matrix Tensor Quart. 21 (1971), 83--84, MathSciNet.  
  29. The Explicit Inverse of a Tridiagonal Matrix  
    P. Schlegel  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), p. 665, Jstor.  
  30. 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.  
  31. 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.  
  32. 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.  
  33. 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.  
  34. 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.  
  35. 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.  
  36. 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.  
  37. 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.  
  38. 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.  
  39. 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.  
  40. Instability of the elimination method of reducing a matrix to tri-diagonal form.
    Wilkinson, J. H.
    Comput. J. 5 1962 61--70, MathSciNet.  
  41. 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.  
  42. 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