2014.7: Max-Plus Singular Values
2014.7: James Hook (2014) Max-Plus Singular Values.
There is a more recent version of this eprint available. Click here to view it.
Full text available as:
|PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader|
In this paper we prove a new characterization of the max-plus singular values of a max- plus matrix, as the max-plus eigenvalues of an associated max-plus matrix pencil. This new characterization allows us to compute max-plus singular values quickly and accurately. As well as capturing the asymptotic behavior of the singular values of classical matrices whose entries are exponentially parameterized we show experimentally that max-plus singular values give order of magnitude approximations to the classical singular values of parameter independent classical matrices. We also discuss Hungarian scaling, which is a diagonal scaling strategy for preprocessing classical linear systems. We show that Hungarian scaling can dramatically reduce the d-norm condition number and that this action can be explained using our new theory for max-plus singular values.
|Item Type:||MIMS Preprint|
|Uncontrolled Keywords:||max-plus algebra, singular values, Hungarian scaling, optimal assignment, maximal matching, network flow algorithm, eigenvalues, matrix condition number|
|Subjects:||MSC 2000 > 15 Linear and multilinear algebra; matrix theory|
MSC 2000 > 41 Approximations and expansions
MSC 2000 > 65 Numerical analysis
MSC 2000 > 90 Operations research, mathematical programming
|Deposited By:||Mr James Hook|
|Deposited On:||12 March 2014|
Available Versions of this Item
- Max-Plus Singular Values (deposited 21 September 2015)
- Max-Plus Singular Values (deposited 12 March 2014) [Currently Displayed]