Bibliography for

Cholesky, Doolittle and Crout Factorization

short

  1. Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines.
    Choi, J.; Dongarra, J.J.; Whaley, R.C.
    Scientific programming, 1996, vol. 5, no. 3, pp. 173, Ingenta.  
  2. The Cholesky Decomposition of P - pp'  
    Richard William Farebrother  
    Journal of the Royal Statistical Society. Series B (Methodological), Vol. 56, No. 4. (1994), p. 727, Jstor.  
  3. Recurrent neural networks for LU decomposition and Cholesky factorization.
    Wang, J.; Wu, G.
    Math. Comput. Modelling 18 (1993), no. 6, 1--8, MathSciNet.  
  4. 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.  
  5. A new modified Cholesky factorization.
    Schnabel, Robert B.; Eskow, Elizabeth
    SIAM J. Sci. Statist. Comput. 11 (1990), no. 6, 1136--1158, MathSciNet.  
  6. On Some Determinant Inequalities and Cholesky Factorization
    Panos M. Pardalos    
    Mathematics Magazine: Volume 61, Number 3, (1988), Pages: 170-171.   
  7. Fast Gauss-Doolittle matrix triangulation.
    Williams, F. W.; Kennedy, D.
    Comput. & Structures 28 (1988), no. 2, 143--148, MathSciNet.  
  8. A note on rounding-error analysis of Cholesky factorization.
    Kielbasi'nski, Andrzej
    Linear Algebra Appl. 88/89 (1987), 487--494, MathSciNet.  
  9. Best Equivariant Estimators of a Cholesky Decomposition  
    Morris L. Eaton, Ingram Olkin  
    Annals of Statistics, Vol. 15, No. 4. (Dec., 1987), pp. 1639-1650, Jstor.  
  10. Refined Error Analyses of Cholesky Factorization  
    Jean Meinguet  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 6. (Dec., 1983), pp. 1243-1250, Jstor.  
  11. 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.  
  12. 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, Jstor.  
  13. Calculation of Expected Mean Squares by the Abbreviated Doolittle and Square Root Methods  
    D. W. Gaylor, H. L. Lucas, R. L. Anderson  
    Biometrics, Vol. 26, No. 4. (Dec., 1970), pp. 641-655, Jstor.  
  14. A Modified Doolittle Approach for Multiple and Partial Correlation and Regression  
    Richard J. Foote  
    Journal of the American Statistical Association, Vol. 53, No. 281. (Mar., 1958), pp. 133-143, Jstor.  
  15. The Doolittle Method and the Fitting of Polynomials to Weighted Data (in Miscellanea)  
    P. G. Guest  
    Biometrika, Vol. 40, No. 1/2. (Jun., 1953), pp. 229-231, Jstor.  
  16. The Doolittle method and the fitting of polynomials to weighted data   
    P. G. Guest  
    Biometrika, Vol. 40, No. 1/2. (Jun., 1953), pp. 229-231, Jstor.  
  17. Accuracy in the Doolittle solution  
    Dickson H. Leavens
    Econometrica, Vol. 15, No. 1. (Jan., 1947), pp. 45-50, Jstor.  
  18. Note on the Doolittle solution  
    Nancy Bruner  
    Econometrica, Vol. 15, No. 1. (Jan., 1947), pp. 43-44, Jstor.  
  19. Correlation concepts and the Doolittle method  
    Dudley J. Cowden
    Journal of the American Statistical Association, Vol. 38, No. 223. (Sep., 1943), pp. 327-334, Jstor.  
  20. The Doolittle Technique  
    Paul S. Dwyer  
    Annals of Mathematical Statistics, Vol. 12, No. 4. (Dec., 1941), pp. 449-458, Jstor.  
  21. Fundamental Formulas for the Doo-Little Method, Using Zero-Order Correlation Coefficients  
    Harold D. Griffin
    Annals of Mathematical Statistics, Vol. 2, No. 2. (May, 1931), pp. 150-153, Jstor.  
  22. Doolittle Versus the Kelley-Salisbury Iteration Method for Computing Multiple Regression Coefficients (in Notes)  
    Truman L. Kelley, Quinn McNemar
    Journal of the American Statistical Association, Vol. 24, No. 166. (Jun., 1929), pp. 164-169, Jstor.  
  23. The Doolittle Method for Solving Multiple Correlation Equations Versus the Kelley-Salisbury "Iteration" Method (in Notes)  
    H. R. Tolley, Mordecai Ezekiel
    Journal of the American Statistical Association, Vol. 22, No. 160. (Dec., 1927), pp. 497-500, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003