Bibliography for

Triangular Systems and Back Substitution

 Return to Numerical Methods - Numerical Analysis

 

  1. Design and Implementation of a General Parallel Divide-and-Conquer Algorithm for Triangular Matrix Inversion
    Nasri, W.; Mahjoub, Z.
    International Journal of Parallel and Distributed Systems and Networks, 2002, vol. 5, no. 1, pp. 35-42, Ingenta.  
  2. The computation of linear triangular system matrices in the finite element method
    Olayi, GA
    Global Journal of Pure and Applied Sciences, 2001, vol. 7, no. 1, pp. 173-178, Ingenta.  
  3. Triangular Matrix Representations.
    Birkenmeier, Gary F.; Heatherly, Henry E.; Park, Jae Keol
    Journal of Algebra, 2000, vol. 230, no. 2, pp. 558, Ingenta.   
  4. The inverse of a lower triangular matrix.   
    Mallik, Ranjan K.  
    Int. J. Math. Game Theory Algebra 8 (1999), no. 4, 167--174, MathSciNet.  
  5. The formal derivation of parallel triangular system solvers using a coordination-based design method.
    Chaudron, MRV; vanDuin, ACN
    Parallel computing, 1998, vol. 24, no. 7, pp. 1023, Ingenta.  
  6. The triangular matrices of Gaussian elimination and related decompositions.
    Stewart, GW
    IMA journal of numerical analysis, 1997, vol. 17, no. 1, pp. 7, Ingenta.  
  7. Scheduling of the DAG Associated with Pipeline Inversion of Triangular Matrices.
    Djamegni, CT; Tchuente, M
    Parallel processing letters, 1996, vol. 6, no. 1, pp. 13, Ingenta.  
  8. Stability of Parallel Triangular System Solvers.
    Higham, NJ
    SIAM journal on scientific and statistical compu, 1995, vol. 16, no. 2, pp. 400, Ingenta.  
  9. Improved Parallel Solution of a Triangular Linear System.
    Pan, VY
    Computers & mathematics with applications, 1994, vol. 27, no. 11, pp. 41, Ingenta.  
  10. Parallel algorithms for sparse triangular system solution.
    Kumar, PS; Kumar, MK; Basu, A
    Parallel computing, 1993, vol. 19, no. 2, pp. 187, Ingenta.  
  11. How to Store a Triangular Matrix.
    LaPaugh, A.S.; Lipton, R.J.; Sandberg, J.S.
    Ieee transactions on computers, 1992, vol. 41, no. 7, pp. 896, Ingenta.   
  12. Parallel Triangular System Solving on a Mesh Network of Transputers.
    Bisseling, RH; vandeVorst, JGG
    Siam journal on scientific and statistical compu, 1991, vol. 12, no. 4, pp. 787, Ingenta.  
  13. An Algorithm For Decomposing a Class of Matrices into Lower and Upper Triangular Matrices.
    Adhami, RR; Lanteign, DJ; Gregory, DA
    Journal of the Franklin Institute, 1990, vol. 327, no. 4, pp. 573, Ingenta.  
  14. The Accuracy of Solutions to Triangular Systems  
    Nicholas J. Higham  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 5. (Oct., 1989), pp. 1252-1265, Jstor.  
  15. Upper Triangularization of Matrices by Permutations and Lower Triangular Similarity Transformations.
    Bart, H
    Linear algebra and its applications, 1988, vol. 110, no. , pp. 255, Ingenta.  
  16. A Survey of Condition Number Estimation for Triangular Matrices  
    Nicholas J. Higham  
    SIAM Review, Vol. 29, No. 4. (Dec., 1987), pp. 575-596, Jstor.  
  17. The Variance-Covariance Matrix of the Maximum Likelihood Estimator in Triangular Structural Systems: Consistent Estimation (in Notes and Comments)  
    Ingmar R. Prucha  
    Econometrica, Vol. 55, No. 4. (Jul., 1987), pp. 977-978, Jstor.  
  18. Remark AS R44: A Remark on AS 6 and AS7: Triangular Decomposition of a Symmetric Matrix and Inversion of a Positive Semi-Definite Symmetric Matrix (in Statistical Algorithms)  
    P. R. Freeman  
    Applied Statistics, Vol. 31, No. 3. (1982), pp. 336-339, Jstor.  
  19. A Note on the Consistency of the GLS Estimator in Triangular Structural Systems (in Notes and Comments)  
    Robert F. Cotterman  
    Econometrica, Vol. 49, No. 6. (Nov., 1981), pp. 1589-1591, Jstor.  
  20. On the Estimation of Triangular Structural Systems (in Notes and Comments)  
    Kajal Lahiri, Peter Schmidt  
    Econometrica, Vol. 46, No. 5. (Sep., 1978), pp. 1217-1221 , Jstor.  
  21. Remark AS R27: A Remark on Algorithm AS 6: Triangular Decomposition of a Symmetric Matrix (in Statistical Algorithms)  
    J. C. Barrett, M. J. R. Healy  
    Applied Statistics, Vol. 27, No. 3. (1978), pp. 379-380, Jstor.  
  22. Solving Triangular Systems on a Parallel Computer  
    Ahmed H. Sameh, Richard P. Brent  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 6. (Dec., 1977), pp. 1101-1113, Jstor.  
  23. Triangular Factorization and Inversion by Fast Matrix Multiplication  
    James R. Bunch, John E. Hopcroft  
    Mathematics of Computation, Vol. 28, No. 125. (Jan., 1974), pp. 231-236, Jstor.  
  24. Conjugate Points, Triangular Matrices, and Riccati Equations  
    Zeev Nehari  
    Transactions of the American Mathematical Society, Vol. 199. (Nov., 1974), pp. 181-198, Jstor.  
  25. A Packing Problem for Triangular Matrices (in Research Problems)  
    W. Klotz, L. Lucht  
    American Mathematical Monthly, Vol. 79, No. 4. (Apr., 1972), pp. 378-379, Jstor.  
  26. Triangular Matrices and the Cayley-Hamilton Theorem  
    Barker, George Phillip
    Math. Mag. 44 (1971), 34--36, MathSciNet.  
  27. Generalized Inverses of Triangular Matrices  
    Carl D. Meyer, Jr.  
    SIAM Journal on Applied Mathematics, Vol. 18, No. 2. (Mar., 1970), pp. 401-406, Jstor.  
  28. Summability of a Sequence of Fourier Coefficients by a Triangular Matrix Transformation  
    H. P. Dikshit  
    Proceedings of the American Mathematical Society, Vol. 21, No. 1. (Apr., 1969), pp. 10-20, Jstor.  
  29. Iteration of Triangular Matrices (in Technical Notes and Short Papers)  
    Lester J. Senechalle  
    Mathematics of Computation, Vol. 18, No. 88. (Oct., 1964), pp. 651-653, Jstor.  
  30. On Some Summability Methods with Triangular Matrix  
    Otto Szasz  
    The Annals of Mathematics, 2nd Ser., Vol. 46, No. 4. (Oct., 1945), pp. 567-577, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003