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. Triangular skew-symmetric iterative solvers for strongly nonsymmetric positive real linear system of equations
    Krukier, LA; Chikina, LG; Belokon, TV
    Applied Numerical Mathematics, 2002, vol. 41, no. ER1, pp. 89-105, Ingenta.  
  3. Optimal parallelization of a recursive algorithm for triangular matrix inversion on MIMD computers.  
    Nasri, Wahid; Mahjoub, Zaher   
    Parallel Comput. 27 (2001), no. 13, 1767--1782, MathSciNet.  
  4. Completions of triangular matrices: a survey of results and open problems.   
    Rodman, Leiba
    Structured matrices in mathematics, computer science, and engineering, II (Boulder, CO, 1999), 279--293,  Contemp. Math., 281, Amer. Math. Soc., Providence, RI, 2001, MathSciNet.  
  5. 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.  
  6. Eigenvectors of lower triangular matrices.   
    Mallik, Ranjan K.  
    Int. J. Appl. Math. 2 (2000), no. 1, 47--56, MathSciNet.  
  7. Triangular Matrix Representations.
    Birkenmeier, Gary F.; Heatherly, Henry E.; Park, Jae Keol
    Journal of Algebra, 2000, vol. 230, no. 2, pp. 558, Ingenta.   
  8. The Meromorphic Reducibility of a Lienar Triangular ODE System.
    Bruno, AD
    Doklady, Mathematics, Russian Academy of Sciences, 2000, vol. 61, no. 2, pp. 243, Ingenta.  
  9. The inverse of a lower triangular matrix.   
    Mallik, Ranjan K.  
    Int. J. Math. Game Theory Algebra 8 (1999), no. 4, 167--174, MathSciNet.  
  10. Semi-infinite lower-triangular matrices
    Shterenberg, RG
    Vestnik- St Petersburg University Mathematics, 1999, vol. 32, no. 4, pp. 54-55, Ingenta.  
  11. Scalable Parallel Preconditioning with the Sparse Approximate Inverse of Triangular Matrices.
    vanDuin, ACN
    SIAM journal on matrix analysis and applications, 1999, vol. 20, no. 4, pp. 987, Ingenta.  
  12. Products of three triangular matrices.
    Nagarajan, KR; Devasahayam, MP; Soundararajan, T
    Linear algebra and its applications, 1999, vol. 292, no. 1/3, pp. 61, Ingenta.  
  13. Condition numbers of random triangular matrices.   
    Viswanath, D.; Trefethen, L. N.  
    SIAM J. Matrix Anal. Appl. 19 (1998), no. 2, 564--581 (electronic), MathSciNet.  
  14. 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.  
  15. Estimation of a Triangular, Seemingly Unrelated, Regression System by OLS.
    Sentana, E
    Econometric theory, 1998, vol. 14, no. 2, pp. 289, Ingenta.  
  16. Upper triangular similarity of upper triangular matrices.  
    Thijsse, Philip
    Linear Algebra Appl. 260 (1997), 119--149, MathSciNet.  
  17. Estimation of a Triangular, Seemingly Unrelated, Regression System by OLS.
    Sentana, E
    Econometric theory, 1997, vol. 13, no. 3, pp. 463, Ingenta.  
  18. The triangular matrices of Gaussian elimination and related decompositions.
    Stewart, GW
    IMA journal of numerical analysis, 1997, vol. 17, no. 1, pp. 7, Ingenta.  
  19. Perturbation Analysis of System Hessenberg and Hessenberg-Triangular Forms.
    Sun, JG
    Linear algebra and its applications, 1996, vol. 241/243, no. , pp. 811, Ingenta.  
  20. 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.  
  21. On the stability of the cyclic reduction without back substitution for tridiagonal systems.(English.English summary)  
    Yalamov,Plamen Y.  
    BIT 35 (1995),no.3,428--447, MathSciNet.  
  22. On a Characterization of Processes by the Independence of Linear Forms in a Triangular System.
    Plucinska, A
    Journal of mathematical sciences., 1995, vol. 76, no. 2, pp. 2320, Ingenta.  
  23. Stability of Parallel Triangular System Solvers.
    Higham, NJ
    SIAM journal on scientific and statistical compu, 1995, vol. 16, no. 2, pp. 400, Ingenta.  
  24. Reduction of a Second-Order Linear System to a Triangular System with Coinciding Diagonal Coefficients.
    Lasunskii, AV
    Differential equations, 1994, vol. 30, no. 6, pp. 912, Ingenta.  
  25. Improved Parallel Solution of a Triangular Linear System.
    Pan, VY
    Computers & mathematics with applications, 1994, vol. 27, no. 11, pp. 41, Ingenta.  
  26. Coarse-Grain Parellelizations of Interval Algorithms Decomposing Dense Matrices and Solving Triangular Systems on Multicomputers: Grobkornige Parallelixierungen von Intervallalgorithmen zur Faktorisierung vollbesetzter Matrizen und zur Losung von Dreieckssystemen auf Multicomputern.
    Reith, R; Ullrich, CP
    Computing, 1994, vol. 53, no. 3/4, pp. 243, Ingenta.  
  27. Parallel algorithms for sparse triangular system solution.
    Kumar, PS; Kumar, MK; Basu, A
    Parallel computing, 1993, vol. 19, no. 2, pp. 187, Ingenta.  
  28. Controllability by Completions of Partial Upper Triangular Matrices.
    Gurvits, L; Rodman, L; Shalom, T
    Mathematics of control, signals, and systems, 1993, vol. 6, no. 1, pp. 30, Ingenta.  
  29. 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.   
  30. Faster Computation of Z-matrices for Triangular Segments in Planar Circuits.
    Lee, SH; Benalla, A; Gupta, KC
    International journal of microwave and millimeter-wave computer-aided engineering, 1992, vol. 2, no. 2, pp. 98, Ingenta.  
  31. A Parallel Algorithm for Toeplitz Triangular Matrices.
    Mingkui, C; Hao, L
    Journal of computational mathematics, 1991, vol. 9, no. 1, pp. 33, Ingenta.  
  32. 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.  
  33. Course Grain Scheduling in Parallel Triangular Factorization and Solution of Power System Matrices.
    Lau, K; Tylavsky, DJ; Bose, A
    Ieee transactions on power systems, 1991, vol. 6, no. 2, pp. 708, Ingenta.  
  34. Eigenvalue Neutrality in Block Triangular Matrices.
    Johnson, CR; Schreiner, EA; Elsner, L
    Linear & multilinear algebra, 1990, vol. 27, no. 4, pp. 289, Ingenta.  
  35. 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.  
  36. 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.  
  37. Updating the Triangular Factorization of a Matrix.
    Nazareth, J. L.
    SIAM journal on matrix analysis and applications, 1989, vol. 10, no. 3, pp. 424, Ingenta.   
  38. Algorithmic fault tolerance for matrix operations on triangular arrays.
    Megson, G.M.; Evans, D.J.
    Parallel computing, 1989, vol. 10, no. 2, pp. 207, Ingenta.   
  39. 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.  
  40. The Rank of Powers of Matrices in a Block Triangular Form.
    Friedland, S
    Linear algebra and its applications, 1988, vol. 107, no. , pp. 17, Ingenta.  
  41. A Survey of Condition Number Estimation for Triangular Matrices  
    Nicholas J. Higham  
    SIAM Review, Vol. 29, No. 4. (Dec., 1987), pp. 575-596, Jstor.  
  42. 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.  
  43. 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.  
  44. 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.  
  45. 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.  
  46. 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.  
  47. 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.  
  48. 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.  
  49. Conjugate Points, Triangular Matrices, and Riccati Equations  
    Zeev Nehari  
    Transactions of the American Mathematical Society, Vol. 199. (Nov., 1974), pp. 181-198, Jstor.  
  50. 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.  
  51. A certain theorem of G. P. Barker on triangular matrices. (Serbo-Croatian)
    Stojakovi'c, Mirko
    Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. 2 (1972), 1--5, MathSciNet.  
  52. Triangular Matrices and the Cayley-Hamilton Theorem  
    Barker, George Phillip
    Math. Mag. 44 (1971), 34--36, MathSciNet.  
  53. Triangular matrices with the isoclinal property.
    Derr, Leroy J.
    Pacific J. Math. 37 (1971), 41--43, MathSciNet.  
  54. Generalized Inverses of Triangular Matrices  
    Carl D. Meyer, Jr.  
    SIAM Journal on Applied Mathematics, Vol. 18, No. 2. (Mar., 1970), pp. 401-406, Jstor.  
  55. 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.  
  56. A note on total equivalence of triangular matrices.
    Basu, S. K.
    Rend. Circ. Mat. Palermo (2) 16 1967 81--86, MathSciNet.  
  57. On triangular matrices.
    Kurepa, Dbar uro
    Glasnik Mat.-Fiz. Astronom. Ser. II Dru\v stvo Mat. Fiz. Hrvatske 20 1965 3--22, MathSciNet.  
  58. 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.  
  59. 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