QZ algorithm

*To*: mathgroup at smc.vnet.net*Subject*: [mg25016] QZ algorithm*From*: "Luther Flippen" <lflippen at arl.army.mil>*Date*: Fri, 1 Sep 2000 01:09:50 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

To whomever can help me: I have a question which I originally posed to Mathematica support (see below). Essentially, I would like to compute generalized eigenvalues/eigenvectors for a matrix pencil (pair of matrices) without a priori constraints upon the matrices (such as positive definiteness). The QZ algorithm is the standard one for this, but I cannot find it for use in Mathematica and I would prefer not to have to program it myself (even though I could use Golub's book to do so). This algorithm has an implementation in LAPACK in Fortran, but I would then have to invest in a compiler for Windows NT and link it to Mathematica with MathLink (with which I have little experience). Posed to Mathematica support: Question or Problem: Mathematica has the functions for obtaining eigenvalues/eigenvectors of individual matrices, but I would like to be able to compute generalized eigenvalues/eigenvectors for matrix pencils (pairs of matrices) WITHOUT any special requirements such as positive definiteness. The standard algorithm for this is the QZ algorithm described in Golub's book on matrix methods. How can I access this capability within Mathematica without having to program it from scratch myself. (A built-in version would be far more efficient than anything I could program in Mathematica anyway.) They suggested that I try mathgroup. Dan Flippen - Dr. L. D. Flippen, Jr. (Dan) US Army Research Lab Sensor Integration Branch ATTN: AMSRL-SE-SS phone: 301-394-1003 2800 Powder Mill Road fax: 301-394-4605 Adelphi, MD 20783-1197 email: lflippen at arl.army.mil Bldg. 204, Room 3C094