Bibliography for Ill-Conditioned Linear Systems

short

  1. Inversion error, condition number, and approximate inverses of uncertain matrices
    El Ghaoui, L.
    Linear Algebra and Its Applications, 2001, vol. 343-344, pp. 171-193, Ingenta
  2. Condition number and determinant of a matrix. (Spanish)
    Lemagne Pérez, Jorge
    Investigación Oper. 21 (2000), no. 1, 27--31, MathSciNet.  
  3. Pin-Pointing Solution of Ill-Conditioned Square Systems of Linear Equations
    Volokh, K. Y.
    Applied Mathematics Letters, 2000, vol. 13, no. ER7, pp. 119-124, Ingenta
  4. Extrapolation techniques for ill-conditioned linear systems.
    Brezinski, C.; Redivo-Zaglia, M.; Seatzu, S.
    Numerische mathematik, 1998, vol. 81, no. 1, pp. 1, Ingenta
  5. Condition numbers of random triangular matrices.
    Viswanath, D.; Trefethen, L. N.
    SIAM J. Matrix Anal. Appl. 19 (1998), no. 2, 564--581 (electronic), MathSciNet.  
  6. A Simple Estimate of the Condition Number of a Linear System   
    Heinrich W. Guggenheimer, Alan S. Edelman, Charles R. Johnson   
    College Math Journal: Volume 26, Number 1, (1995), Pages: 2-5, Ingenta
  7. Round-off, Batting Averages, and Ill-Conditioning  
    Edward Rozema  
    College Math Journal: Volume 25, Number 4, (1994), Pages: 314-317   
  8. On the Distribution of a Scaled Condition Number  
    Alan Edelman  
    Mathematics of Computation, Vol. 58, No. 197. (Jan., 1992), pp. 185-190, Jstor.  
  9. A method for solving ill-conditioned systems of linear algebraic equations.
    Abramov, A.A.
    Computational mathematics and mathematical physics, 1991, vol. 31, no. 4, pp. 1, Ingenta
  10. Assessing the Effects of Multiple Rows on the Condition Number of a Matrix (in Theory and Methods)  
    Ali S. Hadi, Martin T. Wells  
    Journal of the American Statistical Association, Vol. 85, No. 411. (Sep., 1990), pp. 786-792, Jstor.  
  11. Estimators of the condition number of matrices. (Spanish)
    González, G.; Vargas, C.
    XXIInd National Congress of the Mexican Mathematical Society (Spanish) (Puebla, 1989), 47--64, Aportaciones Mat. Comun., 8, Soc. Mat. Mexicana, México, 1990, MathSciNet.  
  12. Improved Condition Number for Spectral Methods  
    Wilhelm Heinrichs  
    Mathematics of Computation, Vol. 53, No. 187. (Jul., 1989), pp. 103-119, Jstor.  
  13. A Survey of Condition Number Estimation for Triangular Matrices  
    Nicholas J. Higham  
    SIAM Review, Vol. 29, No. 4. (Dec., 1987), pp. 575-596, Jstor.  
  14. A Simple Estimate of the Condition Number of a Linear System  
    Heinrich W. Guggenheimer, Alan S. Edelman, Charles R. Johnson  
    College Math Journal: Volume 26, Number 1, (1995), Pages: 2-5.
  15. Ill-conditioning: A constant Surprise in Computational Mathematics   
    Bruce H. Edwards and Patricia L. Sharpe   
    College Math Journal: Volume 16, Number 2, (1985), Pages: 141-148.   
  16. Efficient algorithms for computing the condition number of a tridiagonal matrix.
    Higham, Nicholas J.
    SIAM J. Sci. Statist. Comput. 7 (1986), no. 1, 150--165, MathSciNet.  
  17. The Condition Number of Equivalence Transformations that Block Diagonalize Matrix Pencils  
    James Demmel  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 3. (Jun., 1983), pp. 599-610, Jstor.  
  18. Tricks or Treats with the Hilbert Matrix
    Man-Duen Choi
    American Mathematical Monthly, Vol. 90, No. 5. (May, 1983), pp. 301-312, Jstor.  
  19. An Estimate for the Condition Number of a Matrix  
    A. K. Cline, C. B. Moler, G. W. Stewart, J. H. Wilkinson  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 2. (Apr., 1979), pp. 368-375, Jstor.  
  20. On the Condition Number of Local Bases for Piecewise Cubic Polynomials  
    J. M. Varah  
    Mathematics of Computation, Vol. 31, No. 137. (Jan., 1977), pp. 37-44, Jstor.  
  21. Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form  
    G. H. Golub, J. H. Wilkinson  
    SIAM Review, Vol. 18, No. 4. (Oct., 1976), pp. 578-619, Jstor.  
  22. On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed Problems  
    J. M. Varah  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 2. (Apr., 1973), pp. 257-267, Jstor.  
  23. An Algorithm for the Ill-Conditioned Generalized Eigenvalue Problem  
    G. Fix, R. Heiberger  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 1. (Mar., 1972), pp. 78-88, Jstor.  
  24. Some Elementary Properties of Ill Conditioned Matrices and Linear Equations
    N. S. Mendelsohn
    American Mathematical Monthly, Vol. 63, No. 5. (May, 1956), pp. 285-295, Jstor.  
  25. Computational problems concerning the Hilbert matrix.    
    Todd, John    
    J. Res. Nat. Bur. Standards Sect. B 65B 1961 19--22, MathSciNet.  
  26. Effect of propagated error on inverse of Hilbert matrix.    
    Atta, Susie E.     
    J. Assoc. Comput. Mach. 4 (1957), 36--40, MathSciNet.  
  27. On the Hilbert Matrix  
    Tosio Kato  
    Proceedings of the American Mathematical Society, Vol. 8, No. 1. (Feb., 1957), pp. 73-81, Jstor.  
  28. Some Elementary Properties of Ill Conditioned Matrices and Linear Equations  
    N. S. Mendelsohn  
    American Mathematical Monthly, Vol. 63, No. 5. (May, 1956), pp. 285-295, Jstor.  
  29. Solving Systems of Linear Equations With a Positive Definite, Symmetric, but Possibly Ill-Conditioned Matrix  
    James D. Riley  
    Mathematical Tables and Other Aids to Computation, Vol. 9, No. 51. (Jul., 1955), pp. 96-101, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003