Thread View: sci.math.num-analysis
9 messages
9 total messages
Started by Craig Armour
Sun, 20 Jun 1999 00:00
Singular Value Decomposition
Author: Craig Armour
Date: Sun, 20 Jun 1999 00:00
Date: Sun, 20 Jun 1999 00:00
23 lines
1582 bytes
1582 bytes
Hi, I need to write a paper on the use of Singular value Decomposition in numerical Algebra for numerical maths. The main problem I'm having is finding a paper or the sort which describes the svd w.r.t other algorithms interms of performance and various problems. I realise SVD's are great for overconditioned problmes, but how are they better than say a QR factorization. As far as I can figure, alot of algorithms use QR and the sort to compute the svd. what about w.r.t eigen value problems. In short, I have a lot of info telling me that SVD's are great for overconditioned systems and least squares but not much else. Is this the only use of SVD's? for least squares style problems??? Cheers Craig -- Craig Armour c.armour@cltr.uq.edu.au System Administrator Joyce Ackroyd Building Language Lab, University of Queensland phone 33656916 Comments are my own and not of my employer
Re: Singular Value Decomposition
Author: Peter Schroeder
Date: Sun, 20 Jun 1999 00:00
Date: Sun, 20 Jun 1999 00:00
5 lines
851 bytes
851 bytes
Hi Craig, the book "Matrix Computations" by Golub and Van Loan is a good reference. Peter
Re: Singular Value Decomposition
Author: Bernard Danloy
Date: Mon, 21 Jun 1999 00:00
Date: Mon, 21 Jun 1999 00:00
25 lines
1828 bytes
1828 bytes
In article <376C787E.939C192B@kings.uq.edu.au>, c.armour@uq.net.au wrote๏ฟฝ: : Hi, : : I need to write a paper on the use of Singular value Decomposition in : numerical Algebra for numerical maths. The main problem I'm having is : finding a paper or the sort which describes the svd w.r.t other : algorithms interms of performance and various problems. : : I realise SVD's are great for overconditioned problmes, but how are they : better than say a QR factorization. As far as I can figure, alot of : algorithms use QR and the sort to compute the svd. what about w.r.t : eigen value problems. : : In short, I have a lot of info telling me that SVD's are great for : overconditioned systems and least squares but not much else. Is this : the only use of SVD's? for least squares style problems??? : Not many people know it but all orthogonal polynomials satisfy coupled 2-terms recurrences, so that their zeros are related with the singular values of a bidiagonal matrix ; SVD is therefore an essential tool in the numerical construction of Gaussian quadratures. Bernard Danloy
Re: Singular Value Decomposition
Author: Kevin G. Rhoads
Date: Mon, 21 Jun 1999 00:00
Date: Mon, 21 Jun 1999 00:00
11 lines
931 bytes
931 bytes
In matrix inversion, nearly singular values result in rapid loss of precision in machine calculation. The SVD approach has been adapted to improving accuracy and precision in machine inversion of nearly-singular matrices. So you have a whole arena of machine-computation literature to check also. -- Kevin G. Rhoads, Ph.D. (Linearity is a convenient fiction.) T_Rhoads@NO_SPAM.MSN.com krhoads@NO_SPAM.cmpnetmail.com
Re: Singular Value Decomposition
Author: Louis M. Pecora
Date: Mon, 21 Jun 1999 00:00
Date: Mon, 21 Jun 1999 00:00
25 lines
1949 bytes
1949 bytes
In article <danloy-2106991346450001@quadra.anma.ucl.ac.be>, danloy@anma.ucl.ac.be (Bernard Danloy) wrote: > Not many people know it but all orthogonal polynomials satisfy coupled > 2-terms recurrences, so that their zeros are related with the singular > values of a bidiagonal matrix ; Hi Bernard, This is very interesting. Can you point to a reference where I can read more? Thanks. -- Louis M. Pecora pecora@anvil.nrl.navy.mil == My views and opinions are not those of the U.S. Navy. == == No Spamming or Soliciting -- both are illegal at this site == --------------------------------------------------------------------- Check out our Nonlinear Web site: http://chaos-mac.nrl.navy.mil/ -------------------------------------------------------------------- ------------------------------------------------------------------------ * The 5th Experimental Chaos Conference June 1999. Check it out at http://www.physics.gatech.edu/ecc5/#proceedings * The 4th Experimental Chaos Conference Sessions & Abstracts Online: http://natasha.umsl.edu/Exp_Chaos4, proceedings now available. ---------------------------------------------------------------------
Re: Singular Value Decomposition
Author: Bernard Danloy
Date: Mon, 21 Jun 1999 00:00
Date: Mon, 21 Jun 1999 00:00
29 lines
1931 bytes
1931 bytes
In article <pecora-2106990936270001@pecora7600.nrl.navy.mil>, pecora@zoltar.nrl.navy.mil (Louis M. Pecora) wrote ๏ฟฝ: : In article <danloy-2106991346450001@quadra.anma.ucl.ac.be>, : danloy@anma.ucl.ac.be (Bernard Danloy) wrote: : : > Not many people know it but all orthogonal polynomials satisfy coupled : > 2-terms recurrences, so that their zeros are related with the singular : > values of a bidiagonal matrix ; : : Hi Bernard, : : This is very interesting. Can you point to a reference where I can read : more? Thanks. --------------------------------------------------------------------- Sorry, i don't have many pointers ... The coupled recurrences are the system (2.6) in a paper of mine in Math. Comp. vol. 27 ( 1973 ) p. 863 Rewriting the system by means of a bidiagonal matrix ( the singular values of which are the shifted zeroes of the n-th orthogonal polynomial ) is a 10-years old unpublished result ... But recently, similar results have been obtained independently by Dirk Laurie and i believe you should find something in a coming issue of JCAM. Bernard Danloy
Re: Singular Value Decomposition
Author: Louis M. Pecora
Date: Mon, 21 Jun 1999 00:00
Date: Mon, 21 Jun 1999 00:00
36 lines
2483 bytes
2483 bytes
In article <danloy-2106991659300001@quadra.anma.ucl.ac.be>, danloy@anma.ucl.ac.be (Bernard Danloy) wrote: > : Hi Bernard, > : > : This is very interesting. Can you point to a reference where I can read > : more? Thanks. > --------------------------------------------------------------------- > > Sorry, i don't have many pointers ... > > The coupled recurrences are the system (2.6) in a paper of mine in Math. > Comp. vol. 27 ( 1973 ) p. 863 > > Rewriting the system by means of a bidiagonal matrix ( the singular values > of which are the shifted zeroes of the n-th orthogonal polynomial ) is a > 10-years old unpublished result ... > > But recently, similar results have been obtained independently by Dirk > Laurie and i believe you should find something in a coming issue of JCAM. OK. Will check it. -- Louis M. Pecora pecora@anvil.nrl.navy.mil == My views and opinions are not those of the U.S. Navy. == == No Spamming or Soliciting -- both are illegal at this site == --------------------------------------------------------------------- Check out our Nonlinear Web site: http://chaos-mac.nrl.navy.mil/ -------------------------------------------------------------------- ------------------------------------------------------------------------ * The 5th Experimental Chaos Conference June 1999. Check it out at http://www.physics.gatech.edu/ecc5/#proceedings * The 4th Experimental Chaos Conference Sessions & Abstracts Online: http://natasha.umsl.edu/Exp_Chaos4, proceedings now available. ---------------------------------------------------------------------
Re: Singular Value Decomposition
Author: Robin Becker
Date: Mon, 21 Jun 1999 00:00
Date: Mon, 21 Jun 1999 00:00
23 lines
1590 bytes
1590 bytes
In article <376C787E.939C192B@kings.uq.edu.au>, Craig Armour <c.armour@kings.uq.edu.au> writes >Hi, > >I need to write a paper on the use of Singular value Decomposition in >numerical Algebra for numerical maths. The main problem I'm having is >finding a paper or the sort which describes the svd w.r.t other >algorithms interms of performance and various problems. > >I realise SVD's are great for overconditioned problmes, but how are they >better than say a QR factorization. As far as I can figure, alot of >algorithms use QR and the sort to compute the svd. what about w.r.t >eigen value problems. > >In short, I have a lot of info telling me that SVD's are great for >overconditioned systems and least squares but not much else. Is this >the only use of SVD's? for least squares style problems??? > >Cheers >Craig -- Robin Becker
Re: Singular Value Decomposition
Author: Robin Becker
Date: Tue, 22 Jun 1999 00:00
Date: Tue, 22 Jun 1999 00:00
26 lines
1821 bytes
1821 bytes
In article <8mtuqCAENrb3EwoQ@jessikat.demon.co.uk>, Robin Becker <robin@jessikat.demon.co.uk> writes >In article <376C787E.939C192B@kings.uq.edu.au>, Craig Armour ><c.armour@kings.uq.edu.au> writes >>Hi, >> >>I need to write a paper on the use of Singular value Decomposition in >>numerical Algebra for numerical maths. The main problem I'm having is >>finding a paper or the sort which describes the svd w.r.t other >>algorithms interms of performance and various problems. >> >>I realise SVD's are great for overconditioned problmes, but how are they >>better than say a QR factorization. As far as I can figure, alot of >>algorithms use QR and the sort to compute the svd. what about w.r.t >>eigen value problems. >> >>In short, I have a lot of info telling me that SVD's are great for >>overconditioned systems and least squares but not much else. Is this >>the only use of SVD's? for least squares style problems??? >> >>Cheers >>Craig > sorry for the spurious post, maybe I've got some kind of problem. -- Robin Becker
Thread Navigation
This is a paginated view of messages in the thread with full content displayed inline.
Messages are displayed in chronological order, with the original post highlighted in green.
Use pagination controls to navigate through all messages in large threads.
Back to All Threads