Bibliography for the Inverse Matrix

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  1. The inverse of a tridiagonal matrix
    Mallik, R. K.
    Linear Algebra and Its Applications, 2001, vol. 325, no. ER1-3, pp. 109-139, Ingenta.  
  2. Finding a Determinant and Inverse Matrix by Bordering  
    Yong-Zhuo Chen, Richard F. Melka  
    College Math Journal: Volume 29, Number 1, Pages: 38-39, 1998.  
  3. Stable calculation via regularization of the Moore-Penrose generalized inverse matrix. II. Revision. (Spanish)
    López Estrada, Jesús; Guerra Ones, Valia
    Cienc. Mat. (Havana) 16 (1998), no. 2, 169--172, MathSciNet.  
  4. A New Matrix Inverse  
    C. Krattenthaler  
    Proceedings of the American Mathematical Society, Vol. 124, No. 1. (Jan., 1996), pp. 47-59, Jstor.  
  5. A new matrix inverse.
    Krattenthaler, C.
    Proceedings of the american mathematical society, 1996, vol. 124, no. 1, pp. 47, Ingenta.  
  6. Inverse Interval Matrix  
    J. Rohn  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 3. (Jun., 1993), pp. 864-870, Jstor.  
  7. A Matrix Solution to the Inverse Perron-Frobenius Problem  
    P. Gora, A. Boyarsky  
    Proceedings of the American Mathematical Society, Vol. 118, No. 2. (Jun., 1993), pp. 409-414, Jstor.  
  8. A Geometric interpretation of the Columns of the (Pseudo)Inverse of A   
    Melvin Maron, Ghansham Manwani  
    College Math Journal: Volume 24, Number 1, Pages: 73-75, 1993.  
  9. Inverse Interval Matrix.
    Rohn, J.
    SIAM journal on numerical analysis, 1993, vol. 30, no. 3, pp. 864, Ingenta.  
  10. An Exact Cholesky Decomposition and the Generalized Inverse of the Variance-Covariance Matrix of the Multinomial Distribution, with Applications  
    Kunio Tanabe, Masahiko Sagae  
    Journal of the Royal Statistical Society. Series B (Methodological), Vol. 54, No. 1. (1992), pp. 211-219, Jstor.  
  11. Updating the Inverse of a Matrix  
    William W. Hager  
    SIAM Review, Vol. 31, No. 2. (Jun., 1989), pp. 221-239, Jstor.  
  12. Algorithm AS 240: Updating the Inverse of the Dispersion Matrix (in Statistical Algorithms)  
    Yer Van Hui  
    Applied Statistics, Vol. 37, No. 3. (1988), pp. 474-477, Jstor.  
  13. A Matrix Inverse  
    D. M. Bressoud  
    Proceedings of the American Mathematical Society, Vol. 88, No. 3. (Jul., 1983), pp. 446-448, Jstor.  
  14. Hand computation of generalized inverses  
    D. Barr  
    Mathematics Magazine: Volume 58, Number 2, Pages: 102-107, 1985.  
  15. What Infinite Matrices Can Do  
    Wilansky, Albert  
    Mathematics Magazine: Volume 58, Number 5, Pages: 281-283, 1985.  
  16. Self-Inverse Integer Matrices  
    Robert Hanson College  
    Math Journal: Volume 16, Number 3, Pages: 190-198, 1985.  
  17. The Inverse of a Totally Positive Bi-Infinite Band Matrix  
    Carl De Boor  
    Transactions of the American Mathematical Society, Vol. 274, No. 1. (Nov., 1982), pp. 45-58, Jstor.  
  18. Integer Matrices Whose Inverses Contain Only Integers  
    Robert Hanson College  
    Math Journal: Volume 13, Number 1, Pages: 18-21, 1982.  
  19. A Generalization of the Formula for Computing the Inverse of a Matrix (in Classroom Notes)  
    Chantal Shafroth  
    American Mathematical Monthly, Vol. 88, No. 8. (Oct., 1981), pp. 614-616, Jstor.  
  20. The Square Root of a 2x2 Matrix  
    Bernard W. Levinger Mathematics  
    Magazine: Volume 53, Number 4, Pages: 222-224, 1980.  
  21. Corrections to "Estimation of the Inverse Covariance Matrix: Random Mixtures of the Inverse Wishart Matrix and the Identity"  
    L. R. Haff  
    Annals of Statistics, Vol. 9, No. 5. (Sep., 1981), p. 1132, Jstor.  
  22. Estimation of the Inverse Covariance Matrix: Random Mixtures of the Inverse Wishart Matrix and the Identity  
    L. R. Haff  
    Annals of Statistics, Vol. 7, No. 6. (Nov., 1979), pp. 1264-1276, Jstor.  
  23. On Updating the Inverse of an Adjusted Matrix (in Technical Note)  
    O. D. Anderson  
    The Journal of the Operational Research Society, Vol. 29, No. 1. (Jan., 1978), pp. 85-86, Jstor.  
  24. A Note on a Matrix Inversion in Multiple Exponential Smoothing (in Notes, Comments and Queries)  
    E. McKenzie, M. M. Peterson  
    Journal of the Royal Statistical Society. Series B (Methodological), Vol. 40, No. 2. (1978), pp. 182-183, Jstor.  
  25. Approximate Matrix Inversion (in Technical Notes)  
    R. B. Flavell  
    Operational Research Quarterly (1970-1977), Vol. 28, No. 3, Part 1. (1977), pp. 517-520, Jstor.  
  26. Inverse Iteration on Defective Matrices  
    Nai-fu Chen  
    Mathematics of Computation, Vol. 31, No. 139. (Jul., 1977), pp. 726-732, Jstor.  
  27. Which Nonnegative Matrices are Self-Inverse ?  
    Frank Harary, Henryk Minc  
    Mathematics Magazine: Volume 49, Number 2, Pages: 91-92, 1976.  
  28. Computing the Diagonal Elements and Inverse of a Large Numerator Relationship Matrix  
    R. L. Quaas  
    Biometrics, Vol. 32, No. 4. (Dec., 1976), pp. 949-953, Jstor.  
  29. A Simple Method for Computing the Inverse of a Numerator Relationship Matrix Used in Prediction of Breeding Values  
    C. R. Henderson  
    Biometrics, Vol. 32, No. 1. (Mar., 1976), pp. 69-83, Jstor.  
  30. Singular Value Decomposition and the Moore-Penrose Inverse of Bordered Matrices  
    Robert E. Hartwig  
    SIAM Journal on Applied Mathematics, Vol. 31, No. 1. (Jul., 1976), pp. 31-41, Jstor.  
  31. A Note on a Property of the Inverse of a Bordered Matrix and Its Implication for the Theory of Portfolio Selection (in Communications)  
    M. W. Jones-Lee  
    The Journal of Financial and Quantitative Analysis, Vol. 9, No. 6. (Dec., 1974), pp. 1081-1087, Jstor.  
  32. Demonstrating the Conceptual Significance of the Matrix Inverse (in Education Research and Academic Notes)  
    Edwin Heard, Constantine Konstans, James Don Edwards  
    The Accounting Review, Vol. 49, No. 2. (Apr., 1974), pp. 377-381, Jstor.  
  33. A Comment on Syminv: An Algorithm for the Inversion of a Positive Definite Matrix by the Cholesky Decomposition (in Computer Algorithm)  
    J. Stewart  
    Econometrica, Vol. 42, No. 4. (Jul., 1974), p. 771, Jstor.  
  34. 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.  
  35. Erratum: The Generalized Inverse of a Nonnegative Matrix  
    R. J. Plemmons, R. E. Cline  
    Proceedings of the American Mathematical Society, Vol. 39, No. 3. (Aug., 1973), p. 651, Jstor.  
  36. Some More Representations for the Generalized Inverse of a Partitioned Matrix  
    J. V. Venugopala Rao  
    SIAM Journal on Applied Mathematics, Vol. 24, No. 2. (Mar., 1973), pp. 272-276, Jstor.  
  37. Block Toeplitz Matrix Inversion  
    Hirotugu Akaike  
    SIAM Journal on Applied Mathematics, Vol. 24, No. 2. (Mar., 1973), pp. 234-241, Jstor.  
  38. The Generalized Inverse of a Nonnegative Matrix  
    R. J. Plemmons, R. E. Cline  
    Proceedings of the American Mathematical Society, Vol. 31, No. 1. (Jan., 1972), pp. 46-50, Jstor.  
  39. SYMINV: An Algorithm for the Inversion of a Positive Definite Matrix by the Cholesky Decomposition (in Computer Algorithms)  
    Terry Seaks  
    Econometrica, Vol. 40, No. 5. (Sep., 1972), pp. 961-962, pp. 46-50, Jstor.  
  40. A Hyperpower Iterative Method for Computing Matrix Products Involving the Generalized Inverse  
    James M. Garnett III, Adi Ben-Israel, Stephen S. Yau  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 1. (Mar., 1971), pp. 104-109, Jstor.  
  41. Almost Periodicity of the Inverse of a Fundamental Matrix  
    A. M. Fink  
    Proceedings of the American Mathematical Society, Vol. 27, No. 3. (Mar., 1971), pp. 527-528, Jstor.  
  42. An Extension of the Generalized Inverse of a Matrix  
    Randall E. Cline, T. N. E. Greville  
    SIAM Journal on Applied Mathematics, Vol. 19, No. 4. (Dec., 1970), pp. 682-688, Jstor.  
  43. The Explicit Inverse of a Tridiagonal Matrix  
    P. Schlegel  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), p. 665, Jstor.  
  44. 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.  
  45. Short Notes: An Explicit Form of the Moore-Penrose Inverse of an Arbitrary Complex Matrix  
    Sanjo Zlobec  
    SIAM Review, Vol. 12, No. 1. (Jan., 1970), pp. 132-134, Jstor.  
  46. On the Concept of A p-q Generalized Inverse of a Matrix  
    T. G. Newman, P. L. Odell  
    SIAM Journal on Applied Mathematics, Vol. 17, No. 3. (May, 1969), pp. 520-525, Jstor.  
  47. Short Notes: The Nature of the Lack of Uniqueness of Generalized Inverse Matrices  
    N. S. Urquhart  
    SIAM Review, Vol. 11, No. 2. (Apr., 1969), pp. 268-271, Jstor.  
  48. The Calculation of the Eigenvectors of a General Complex Matrix by Inverse Iteration  
    J. M. Varah  
    Mathematics of Computation, Vol. 22, No. 104. (Oct., 1968), pp. 785-791+s1-s13, Jstor.  
  49. Solution of the Equation AX + XB = C by Inversion of an m x m or n x n Matrix  
    Antony Jameson  
    SIAM Journal on Applied Mathematics, Vol. 16, No. 5. (Sep., 1968), pp. 1020-1023, Jstor.   
  50. Short Notes: Computation of Generalized Inverse Matrices which Satisfy Specified Conditions  
    N. S. Urquhart  
    SIAM Review, Vol. 10, No. 2. (Apr., 1968), pp. 216-218, Jstor.   
  51. The Inverse of a Certain Matrix, with an Application (in Notes)  
    Chandan K. Mustafi  
    Annals of Mathematical Statistics, Vol. 38, No. 4. (Aug., 1967), pp. 1289-1292, Jstor.  
  52. Erratum: Generalized Inverse of a Matrix Product  
    T. N. E. Greville  
    SIAM Review, Vol. 9, No. 2. (Apr., 1967), p. 249, Jstor.  
  53. A Direct Method for Generalized Matrix Inversion  
    R. P. Tewarson  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 4. (Dec., 1967), pp. 499-507, Jstor.  
  54. A Method for Computing the Generalized Inverse of a Matrix  
    Ben Noble  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 4. (Dec., 1966), pp. 582-584, Jstor.  
  55. Note on the Computation of the Generalized Inverse of a Matrix  
    F. A. Graybill, C. D. Meyer, R. J. Painter  
    SIAM Review, Vol. 8, No. 4. (Oct., 1966), pp. 522-524, Jstor.  
  56. Note on the Generalized Inverse of a Matrix Product  
    T. N. E. Greville  
    SIAM Review, Vol. 8, No. 4. (Oct., 1966), pp. 518-521, Jstor.  
  57. On the Inversion of a Hilbert Type Matrix  
    William F. Trench, Perry A. Scheinok  
    SIAM Review, Vol. 8, No. 1. (Jan., 1966), pp. 57-61, Jstor.  
  58. Matrix Inversion by Rank Annihilation (in Technical Notes and Short Papers)  
    David J. Edelblute  
    Mathematics of Computation, Vol. 20, No. 93. (Jan., 1966), pp. 149-151, Jstor.  
  59. An Alternate Form of the Generalized Inverse of an Arbitrary Complex Matrix  
    Henry P. Decell, Jr.  
    SIAM Review, Vol. 7, No. 3. (Jul., 1965), pp. 356-358, Jstor.  
  60. An Iterative Method for Computing the Generalized Inverse of an Arbitrary Matrix (in Technical Notes and Short Papers)  
    Adi Ben-Israel  
    Mathematics of Computation, Vol. 19, No. 91. (Jul., 1965), pp. 452-455, Jstor.  
  61. An Application of the Cayley-Hamilton Theorem to Generalized Matrix Inversion  
    Henry P. Decell, Jr.  
    SIAM Review, Vol. 7, No. 4. (Oct., 1965), pp. 526-528, Jstor.  
  62. A Note on a Generalized Inverse of a Matrix with Applications to Problems in Mathematical Statistics  
    C. Radhakrishna Rao  
    Journal of the Royal Statistical Society. Series B (Methodological), Vol. 24, No. 1. (1962), pp. 152-158, Jstor.  
  63. A Set of Matrices whose Inverse have for Elements the Elements of the Original Matrix Divided by the Order of the Matrix (in Classroom Notes)  
    John P. Hoyt  
    American Mathematical Monthly, Vol. 69, No. 3. (Mar., 1962), pp. 221-222, pp. 132-133, Jstor.  
  64. An Application of the Wiener-Kolmogorov Smoothing Theory to Matrix Inversion  
    Manus Foster  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 3. (Sep., 1961), pp. 387-392, Jstor.  
  65. A Comment on Matrix Inversion by Partition  
    George Swift  
    SIAM Review, Vol. 2, No. 2. (Apr., 1960), pp. 132-133, Jstor.  
  66. Matrix Inversion by the Annihilation of Rank  
    Herbert S. Wilf  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 7, No. 2. (Jun., 1959), pp. 149-151, Jstor.  
  67. Matrix Inversion, Its Interest and Application in Analysis of Data  
    G. Greenberg, A. E. Sarhan  
    Journal of the American Statistical Association, Vol. 54, No. 288. (Dec., 1959), pp. 755-766, Jstor.  
  68. The Evaluation of Matrix Inversion Programs  
    Morris Newman, John Todd  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 4. (Dec., 1958), pp. 466-476, Jstor.  
  69. A Note on Matrix Inversion by the Square Root Method  
    David Durand  
    Journal of the American Statistical Association, Vol. 51, No. 274. (Jun., 1956), pp. 288-292, Jstor.  
  70. The Row-Sums of the Inverse Matrix, II (in Mathematical Notes)  
    Albert Wilansky  
    American Mathematical Monthly, Vol. 63, No. 9. (Nov., 1956), pp. 652-653, Jstor.  
  71. Methods of Matrix Inversion  
    Donald Greenspan  
    American Mathematical Monthly, Vol. 62, No. 5. (May, 1955), pp. 303-318, Jstor.  
  72. Monte Carlo Matrix Inversion and Recurrent Events  
    H. P. Edmundson  
    Mathematical Tables and Other Aids to Computation, Vol. 7, No. 41. (Jan., 1953), pp. 18-21, Jstor.  
  73. Scaling and Error Analysis for Matrix Inversion by Partitioning  
    Mark Lotkin, Russell Ramage  
    Annals of Mathematical Statistics, Vol. 24, No. 3. (Sep., 1953), pp. 428-439, Jstor.  
  74. Errata: On Errors in Matrix Inversion  
    Paul S. Dwyer, Frederick V. Waugh  
    Journal of the American Statistical Association, Vol. 48, No. 264. (Dec., 1953), pp. 911-912, Jstor.  
  75. On Errors in Matrix Inversion  
    Paul S. Dwyer, Frederick V. Waugh  
    Journal of the American Statistical Association, Vol. 48, No. 262. (Jun., 1953), pp. 289-319, Jstor.  
  76. A Solution of Simultaneous Linear Equations and Matrix Inversion With High Speed Computing Devices  
    Gabriel G. Bejarano, Bruce R. Rosenblatt  
    Mathematical Tables and Other Aids to Computation, Vol. 7, No. 42. (Apr., 1953), pp. 77-81, Jstor.  
  77. Inverse Matrices in Interpolation (in Classroom Notes)  
    J. P. Ballantine  
    American Mathematical Monthly, Vol. 59, No. 3. (Mar., 1952), pp. 178-180, Jstor.  
  78. The Row-Sums of the Inverse Matrix (in Mathematical Notes)  
    Albert Wilansky  
    American Mathematical Monthly, Vol. 58, No. 9. (Nov., 1951), pp. 614-615, Jstor.  
  79. Computation of the Inverse of a Matrix  
    R. V. Andree  
    American Mathematical Monthly, Vol. 58, No. 2. (Feb., 1951), pp. 87-92, Jstor.  
  80. Note on the Inversion of the Leontief Matrix  
    Julian L. Holley  
    Econometrica, Vol. 19, No. 3. (Jul., 1951), pp. 317-320, Jstor.  
  81. Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix (in Notes)  
    Jack Sherman, Winifred J. Morrison  
    Annals of Mathematical Statistics, Vol. 21, No. 1. (Mar., 1950), pp. 124-127, Jstor.  
  82. Matrix Inversion by a Monte Carlo Method  
    George E. Forsythe, Richard A. Leibler  
    Mathematical Tables and Other Aids to Computation, Vol. 4, No. 31. (Jul., 1950), pp. 127-129, Jstor.  
  83. Inversion of the Leontief Matrix by Power Series  
    Frederick V. Waugh  
    Econometrica, Vol. 18, No. 2. (Apr., 1950), pp. 142-154, Jstor.  
  84. Enlargement Methods for Computing the Inverse Matrix  
    Louis Guttman  
    Annals of Mathematical Statistics, Vol. 17, No. 3. (Sep., 1946), pp. 336-343, Jstor.  
  85. Compact Computation of the Inverse of a Matrix  
    Frederick V. Waugh, Paul S. Dwyer  
    Annals of Mathematical Statistics, Vol. 16, No. 3. (Sep., 1945), pp. 259-271, Jstor.  
  86. Note on the Inversion of a Centrosymmetric Matrix (in Discussions and Notes)  
    Edward Saibel  
    American Mathematical Monthly, Vol. 49, No. 4. (Apr., 1942), pp. 246-248, Jstor.  
  87. A New Method for Obtaining the Inverse Matrix  
    M. D. Bingham  
    Journal of the American Statistical Association, Vol. 36, No. 216. (Dec., 1941), pp. 530-534, Jstor.  
  88. A Rule for Computing the Inverse of a Matrix (in Questions, Discussions, and Notes)  
    A. A. Albert  
    American Mathematical Monthly, Vol. 48, No. 3. (Mar., 1941), pp. 198-199, Jstor.  
  89. The Characteristic Equations of the Adjoint and the Inverse of a Matrix (in Questions and Discussions)  
    H. S. Thurston  
    American Mathematical Monthly, Vol. 38, No. 8. (Oct., 1931), pp. 448-449, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003