

Bibliography
for Ill-Conditioned Linear Systems
short
- 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
- Condition number and
determinant of a matrix. (Spanish)
Lemagne Pérez, Jorge
Investigación Oper. 21 (2000), no. 1, 27--31,
MathSciNet.
- 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
- Extrapolation techniques for
ill-conditioned linear systems.
Brezinski, C.; Redivo-Zaglia, M.; Seatzu, S.
Numerische mathematik, 1998, vol. 81, no. 1, pp. 1,
Ingenta
- Condition numbers of random
triangular matrices.
Viswanath, D.; Trefethen, L. N.
SIAM J. Matrix Anal. Appl. 19 (1998), no. 2, 564--581
(electronic), MathSciNet.
- 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
- Round-off,
Batting Averages, and Ill-Conditioning
Edward Rozema
College Math Journal: Volume 25, Number 4, (1994), Pages:
314-317
- On
the Distribution of a Scaled Condition
Number
Alan Edelman
Mathematics of Computation, Vol. 58, No. 197. (Jan., 1992), pp.
185-190, Jstor.
- 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
- 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.
- 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.
- Improved
Condition Number for Spectral Methods
Wilhelm Heinrichs
Mathematics of Computation, Vol. 53, No. 187. (Jul., 1989), pp.
103-119, Jstor.
- A
Survey of Condition Number Estimation for Triangular
Matrices
Nicholas J. Higham
SIAM Review, Vol. 29, No. 4. (Dec., 1987), pp. 575-596,
Jstor.
- 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.
- 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.
- 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.
- 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.
- Tricks
or Treats with the Hilbert Matrix
Man-Duen Choi
American Mathematical Monthly, Vol. 90, No. 5. (May, 1983), pp.
301-312, Jstor.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Computational problems
concerning the Hilbert matrix.
Todd, John
J. Res. Nat. Bur. Standards Sect. B 65B 1961 19--22,
MathSciNet.
- Effect of propagated error on
inverse of Hilbert matrix.
Atta, Susie E.
J. Assoc. Comput. Mach. 4 (1957), 36--40,
MathSciNet.
- On
the Hilbert Matrix
Tosio Kato
Proceedings of the American Mathematical Society, Vol. 8, No. 1.
(Feb., 1957), pp. 73-81, Jstor.
- 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.
- 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