From pmd@sinai.maths.uq.edu.au Wed Feb 9 12:17 EST 2000 Received: from wasabi.it.uq.edu.au (wasabi [130.102.192.56]) by flute.it.uq.edu.au (8.8.8/8.8.8) with ESMTP id MAA13665 for ; Wed, 9 Feb 2000 12:17:44 +1000 (EST) Received: from bunyip.cc.uq.edu.au (root@bunyip.cc.uq.edu.au [130.102.2.1]) by wasabi.it.uq.edu.au (8.8.7/8.8.7) with ESMTP id MAA13511 for ; Wed, 9 Feb 2000 12:17:45 +1000 (EST) Received: from tamago.csee.uq.edu.au (root@tamago.csee.uq.edu.au [130.102.192.50]) by bunyip.cc.uq.edu.au (8.9.3/8.9.3) with ESMTP id MAA32299 for ; Wed, 9 Feb 2000 12:17:44 +1000 (GMT+1000) Received: from yowie.cc.uq.edu.au (root@yowie.cc.uq.edu.au [130.102.2.2]) by tamago.csee.uq.edu.au (8.9.3/8.9.3) with ESMTP id MAA36849 for ; Wed, 9 Feb 2000 12:17:44 +1000 (EST) Received: from sinai.maths.uq.edu.au (sinai.maths.uq.edu.au [130.102.160.57]) by yowie.cc.uq.edu.au (8.9.3/8.9.3) with ESMTP id MAA32740 for ; Wed, 9 Feb 2000 12:17:44 +1000 (GMT+1000) Received: from localhost (pmd@localhost) by sinai.maths.uq.edu.au (8.8.6/0.0.0) with ESMTP id MAA28297 for ; Wed, 9 Feb 2000 12:15:57 +1000 (EST) Date: Wed, 9 Feb 2000 12:15:54 +1000 (EST) From: Phil Diamond To: Greg Gamble Subject: Re: Real Jordan Form (RJF) In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Mozilla-Status: 0011 X-Status: A Content-Length: 1675 Status: RO > > Great! Will initial coding in MAGMA be ok with you? > Yes. Thanks very much Greg. Try this one below. The eigenvalues are (Matlab): 0.6091 + 0.4507i 0.6091 - 0.4507i 0.8577 + 0.2914i 0.8577 - 0.2914i 0.9982 0.9979 0.6643 0.4109 So the RJF is diag(0.9982,0.9979,0.6643,0.4109,C(0.6091,0.4507),C(0.8577,0.2914)), where C(a,b) is the 2x2 block in the previous post. I only have everything to 4 decimal places from the literature, because small FWL in microprocessors is being used (maybe 12-16 bit max) and they are blown up by matrix operations. For example, the matrix below with the eigenvalues above has a "stability reserve" of only 0.0018 (distance from the unit circle) and is almost unstable. > Perhaps, you could send me these matrices, so that I can use them for test > input. This way you will probably have the required transformation > matrices before I finish the algorithm. > Columns 1 through 7 0.9980 0.0006 0.0701 -3.1902 0.0003 -0.0136 -0.2336 -0.0143 1.0448 -0.2686 -3.0575 0.0151 -0.9260 -0.2229 0 0.0017 0.8574 0.1085 0.0001 -0.0014 -0.4744 0 0.0001 0.0926 1.0056 0 -0.0001 -0.0249 0 -0.0021 0 -1.9597 0.9982 -0.0069 -0.0592 0 0.4251 0 -0.7277 0.0004 0.1705 -0.1427 0 0.0009 0 0.3438 0.0001 -0.0001 0.4232 0 -0.0001 0 0.4240 0 0.0001 0.0523 Column 8 -0.9468 0.8575 -1.9731 -0.1035 -2.0050 -0.1892 -1.7410 0.5073 Cordially, Phil