From: "Alan Miller" Subject: Re: Solving Toeplitz linear systems Date: Sat, 20 Feb 1999 17:35:58 +1100 Newsgroups: sci.op-research,sci.math TOMS algorithm 729 contains a package of algorithms for solving Toeplitz systems, mainly using block methods, for both symmetric and general matrices. It contains a number of serious errors, mainly with array bound violations, but it also assumes that REAL and INTEGER variables have the same word length. It is in Fortran 77. It can be downloaded from your local netlib mirror. I don't know of one in France, but there is one in Britain. A Fortran 90 version with bug corrections is available from my web site. -- Alan Miller, Retired Scientist (Statistician) CSIRO Mathematical & Information Sciences Alan.Miller -at- vic.cmis.csiro.au http://www.ozemail.com.au/~milleraj Didier Henrion wrote in message <36CD3CEE.F5B@laas.fr>... >Hello, > >is there any efficient software available for solving Toeplitz >linear systems of equations such as > >[T0 0 0 > T1 T0 . > . T1 0 > Tn . .. T0 > 0 Tn T1 > . . . > 0 0 Tn] * X = R > >where Ti are given rectangular matrices, R is a given rectangular >matrix and X is a matrix to be found ? > >Any advice is welcome. Thanks in advance. > >------------------------------------------------------------------ > Didier Henrion Phone: +33 5 61 33 69 49 > LAAS-CNRS, Bureau E50 Fax: +33 5 61 33 69 69 > 7, Avenue du Colonel Roche mailto:henrion@laas.fr > 31077 Toulouse, Cedex 4, France http://www.laas.fr/~henrion >------------------------------------------------------------------ ============================================================================== From: Patrice Delmas Subject: matrix inverse Date: Sat, 26 Jun 1999 03:53:56 +0200 Newsgroups: sci.math Hi, Is there someone here who can can help me to find an inverse to this n*n matrix A= |c b a 0............0 a b| |b c b a 0 .. .. .. . 0 a| |a b c b a 0 .. .. .. . 0| |0 a b c b a 0 .. .. . 0| |0 .. 0 a b c b a 0 ..0| |..............................| |0 .. .. .. . 0 a b c b a| |a 0 .. .. .. . 0 a b c b| |b a 0 .. .. .. . 0 a b c| the matrix is quasi-pentadiagonal with a 5 center band lengh : thas is 2 symetric diagonals (a and b) around the c center diagonal thanks Pat ============================================================================== From: Raymond Manzoni Subject: Re: matrix inverse Date: Sat, 26 Jun 1999 23:37:09 +0200 Newsgroups: sci.math Hi Pat, This is called a symmetric Toeplitz matrix. Have a look at the numerical recipes (online) at : http://www.ulib.org/webRoot/Books/Numerical_Recipes/bookc.html Some references may be found too at ; http://www.treasure-troves.com/math/ToeplitzMatrix.html The inverse matrix is of the same kind as the initial one (symmetric and with all the lines "rotations" of the first one). A FFT variant of Levinson's scheme (in N*log(N) instead of N^2) may be found at: http://wwwtg.mp.tudelft.nl/~kees/verslag/node17.html A further reference could be too:"Eigenvector Computation for almost-Unitary-Hessenberg Matrices and Inversion of Szego-Vandermonde Matrices via Discrete Transmission Lines" at http://www.cs.gsu.edu/~matvro/papers/tl2/tl2.html Fortran code for the Levinson(-Durbin ?) recursions may be found at : http://weber.u.washington.edu/~dbp/ABSTRACTS/ctsmii.html An algorithm may be found here : http://www.ms.washington.edu/~s520/chpt-09/indexa.html If all this wasn't enough try +levinson +toeplitz at http://www.altavista.com Hope the "Numerical Recipes" or other will help, Raymond Manzoni