Editing User:Antonio Pino:anotherwiki

Jump to navigation Jump to search
User account "Antonio Pino:anotherwiki" is not registered. Please check if you want to create/edit this page.
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.

Latest revision Your text
Line 1: Line 1:
==a starter==
just experimenting with subpages, more info on [[http://en.wikipedia.org/wiki/Wikipedia:User_pages wikipedia]]
...just experimenting with subpages, more info on [[http://en.wikipedia.org/wiki/Wikipedia:User_pages wikipedia]]
 
[...]
 
After this little holiday (Holy Week), I am back to work on gsoc. As Philip Nienhuis noted on the [http://octave.1599824.n4.nabble.com/Re-Query-for-project-on-improving-matrix-functions-td4669292.html#a4669297 mailing list] there is a fair amount of work done on Matrix Functions by Higham himself. Nonetheless, it was made to work with matlab so the first issue to tack is making Gnu Octave work with it, changing it where necessary. Starting from there, then new algorithms should be introduced to the system.
-------
 
==a note==
First of all, I am still interested in going on with the project.
 
Concerning the algorithms, I have done a review of Golub and Van Loan's chapter on matrix functions (2013) and concluded that: for funm the Schur-Parlett algorithm [0] is the most appropriate, since it seems very reliable (i.e. numerically stable), for expm the new scaling and squaring approach (I hope it is the one Prof. Caliari referred to), while its analog will be used for logm. As for sqrtm, one of the latest results is [3], although a more general p-th root algorithm by Smith [4] or Higham/Lin [5] could do the job. Bear in mind that this response is barely a review of them. If you have a more recent source I would be grateful.
 
Note that today has been strange day for me: the last before a Little intermission of this term (Holy Week). I will need a little time for planning the new tentative time line, and do the new proposal; by the way, as google-melange has frozen here the initial one, I shall put it in the wiki.octave page or here as a comment.
 
Therefore, I will go for compatibility first and then for further improvements.
 
Thank Carnë Draug for the comments, I didn't know Octave already made use of the mctoolbox in the gallery function.
 
Antonio Pino
 
 
[0] P.I. Davies and N.J. Higham (2003). "A Schur-Parlett Algorithm for Computing Matrix Functions", SIAM. J. Matrix Anal. Applic. 25, 464-485. <Vhttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.7.6150&rep=rep1&type=pdf>
 
[1] A.H. Al-Mohy and N.J. Higham (2009). "A New Scaling and Squaring Algorithm for the Matrix Exponential," SIAM J. Matrix Anal. Applic. 31, 970-989 <http://eprints.ma.man.ac.uk/1217/01/covered/MIMS_ep2009_9.pdf>
 
[2] S.H. Cheng, N.J. Higham, C.S. Kenney, and A.J. Laub (2001). "Approximating the Logarithm of a Matrix to Specified Accuracy," SIA M J. Matrix Anal. Applic. 22, 1112- 1125. <http://www.maths.manchester.ac.uk/~higham/narep/narep353.ps.gz>
 
[3] A. Frommer and B. Hashemi (2009). "Verified Computation of Square Roots of a Matrix," Matrix Anal. Applic. 31, 1279-1302. <http://www.researchgate.net/publication/220656516_Verified_Computation_of_Square_Roots_of_a_Matrix>
 
[4] M. I. Smith (2003). "A Schur Algorithm For Computing Matrix Pth Roots", SIAM J. MATRIX ANAL. APPL. 24, 4, 971-989. <http://www.maths.manchester.ac.uk/~higham/narep/narep392.ps.gz>
 
[5] N. J. Higham and L. Lin (2011). "A Schur-Parlett Algorithm for Fractional Powers of a Matrix". Manchester Institute for Mathematical Sciences, School of Mathematics, University of Manchester. <http://eprints.ma.man.ac.uk/1677/01/covered/MIMS_ep2010_91.pdf>
Leave a comment
----
==updated task outline==
 
...moved the definitive version to my wiki, User:Antonio_Pino
Please note that all contributions to Octave may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Octave:Copyrights for details). Do not submit copyrighted work without permission!

To edit this page, please answer the question that appears below (more info):

Cancel Editing help (opens in new window)
Retrieved from "https://wiki.octave.org/User:Antonio_Pino:anotherwiki"