From: stewart@cs.umd.edu (G. W. Stewart)
Newsgroups: sci.math.num-analysis
Subject: Re: inverting a matrix
Keywords: MATRIX, INVERSION, DETERMINANT
Date: 10 Oct 92 15:16:19 GMT
Organization: U of Maryland, Dept. of Computer Science, Coll. Pk., MD 20742

In article <1992Oct9.153538.11360@rpslmc.edu> jwang@rad.rpslmc.edu writes:
>I am looking for a computer program in source code level (prefer in C) for efficient calculation of DETERMINANT and INVERSION of a matrix. 
>
>Thanks for help.
>
>Jinzhao.

Although it may not be the case here, most people who ask how to
invert a matrix or find its determinant are unaware that in most
applications one seldom needs to compute these objects.  The modern
approach is to compute a matrix decomposition, such as the LU
decomposition or the QR decomposition, and use it to solve the
problem.  I am appending a list of readily available books--some
elementary, some advanced--that may be of help.

Pete Stewart

\begin{thebibliography}{10}

\bibitem{abbd:92}
E.~Anderson, Z.~Bai, C.~Bischof, J.~Demmel, J.~Dongarra, J.~Du Croz,
  A.~Greenbaum, S.~Hammarling, A.~McKenney, S.~Ostrouchov, and D.~Sorensen.
\newblock {\em {LAPACK} Users' Guide, Release 1.0}.
\newblock SIAM, Philadelphia, 1992.
\newblock To appear.

\bibitem{bjor:88}
{\AA}.~Bj{\"o}rck.
\newblock {\em Solution of Equations in {$R^N$}}, volume~1 of {\em Least
  Squares Methods: Handbook of Numerical Analysis}.
\newblock North-Holland, 1988.
\newblock Cited in \cite{govl:89}.

\bibitem{covl:88}
T.~Coleman and C.~Van~Loan.
\newblock {\em Handbook for Matrix Computations}.
\newblock {SIAM} Publications, Philadelphia, PA, 1988.
\newblock Cited in \cite{govl:89}.

\bibitem{dbms:79}
J.~J. Dongarra, J.~R. Bunch, C.~B. Moler, and G.~W. Stewart.
\newblock {\em LINPACK User's Guide}.
\newblock SIAM, Philadelphia, 1979.

\bibitem{duer:86}
I.~S. Duff, A.~M. Erisman, and J.~K. Reid.
\newblock {\em Direct Methods for Sparse Matrices}.
\newblock Clarendon Press, Oxford, 1986.

\bibitem{geli:81}
J.~A. George and J.~W.~H. Liu.
\newblock {\em Computer Solution of Large Sparse Positive Definite Systems}.
\newblock Prentice-Hall, Englewood Cliffs, NJ., 1981.
\newblock Cited in {\AA ke Bj\"orck's} bibliography on least squares, which is
  available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.

\bibitem{govl:89}
G.~H. Golub and C.~F. Van~Loan.
\newblock {\em Matrix Computations}.
\newblock Johns Hopkins University Press, Baltimore, Maryland, 2nd edition,
  1989.

\bibitem{hous:64}
A.~S. Householder.
\newblock {\em The Theory of Matrices in Numerical Analysis}.
\newblock Dover Publishing, New York, 1964.
\newblock Originally published by Ginn Blaisdell.

\bibitem{jenn:77a}
A.~Jennings.
\newblock {\em Matrix Computation for Engineers and Scientists}.
\newblock John Wiley and Sons, New York, 1977.
\newblock Cited in \cite{govl:89}.

\bibitem{laha:74}
C.~L. Lawson and R.~J. Hanson.
\newblock {\em Solving Least Squares Problems}.
\newblock Prentice Hall, Englewood Cliffs, New Jersey, 1974.

\bibitem{parl:80}
B.~N. Parlett.
\newblock {\em The Symmetric Eigenvalue Problem}.
\newblock Prentice-Hall, Englewood Cliffs, New Jersey, 1980.

\bibitem{sbdg:76}
B.~T. Smith, J.~M. Boyle, J.~J. Dongarra, B.~S. Garbow, Y.~Ikebe, V.~C. Klema,
  and C.~B. Moler.
\newblock {\em Matrix Eigensystem Routines - EISPACK Guide Lecture Notes in
  Computer Science}.
\newblock Springer-Verlag, New York, 2nd edition, 1976.

\bibitem{stew:73c}
G.~W. Stewart.
\newblock {\em Introduction to Matrix Computations}.
\newblock Academic Press, New York, 1973.

\bibitem{varg:62}
R.~S. Varga.
\newblock {\em Matrix Iterative Analysis}.
\newblock Prentice-Hall, Englewood Cliffs, New Jersey, 1962.

\bibitem{watk:91}
D.~S. Watkins.
\newblock {\em Fundamentals of Matrix Computations}.
\newblock John Wiley \& Sons, New York, 1991.

\bibitem{wilk:63}
J.~H. Wilkinson.
\newblock {\em Rounding Errors in Algebraic Processes}.
\newblock Prentice-Hall, Englewood Cliffs, New Jersey, 1963.

\bibitem{wilk:65}
J.~H. Wilkinson.
\newblock {\em The Algebraic Eigenvalue Problem}.
\newblock Clarendon Press, Oxford, England, 1965.

\bibitem{wire:71}
J.~H. Wilkinson and C.~Reinsch.
\newblock {\em Handbook for Automatic Computation. Vol.~II Linear Algebra}.
\newblock Springer, New York, 1971.

\end{thebibliography}
Newsgroups: sci.math.num-analysis