Anonymous avatar Anonymous committed a015aa7 Draft

Skeel number is added

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biblio/kmvlinalgdecompose.bib

 % This file was created with JabRef 2.3.1.
 % Encoding: UTF-8
 
-@OTHER{Wiki2012,
-  author = {\text{Wikipedia, the free encyclopedia}},
-  language = {English},
-  owner = {majid},
-  timestamp = {2012.08.10},
-  title = {Block \text{LU} decomposition},
-  url = {\url{http://en.wikipedia.org/wiki/Block_LU_decomposition}},
-  year = {2012}
-}
-
 @BOOK{lapackuserguide1999,
   title = {LAPACK Users' guide},
   publisher = {Society for Industrial Mathematics},
   number = {2}
 }
 
+@BOOK{higham1996accuracy,
+  title = {Accuracy and stability of numerical algorithms},
+  publisher = {SIAM},
+  year = {1996},
+  author = {Nicholas J. Higham}
+}
+
 @ARTICLE{higham2000block,
   author = {Nicholas J. Higham and Fran{\c{c}}oise Tisseur},
   title = {A block algorithm for matrix 1-norm estimation, with an application
   number = {2}
 }
 
+@ARTICLE{skeel1980iterative,
+  author = {Skeel, R.D.},
+  title = {Iterative refinement implies numerical stability for Gaussian elimination},
+  journal = {Math. Comp},
+  year = {1980},
+  volume = {35},
+  pages = {817--832},
+  number = {151}
+}
+
 @BOOK{Stran2006,
   title = {Linear Algebra and Its Applications},
   publisher = {Thomson Brooks/Cole Cengage Learning},
   timestamp = {2012.08.08}
 }
 
+@ARTICLE{watkins2002fundamentals,
+  author = {David S. Watkins},
+  title = {Fundamentals of matrix computations},
+  year = {2002},
+  publisher = {John Wiley and Sons}
+}
+

decompose-matrixproperties.tex

-% \documentclass[a4paper,10pt]{extreport}
-% \usepackage{amssymb,amsfonts,amsmath,cite,enumerate}
-% \setcounter{tocdepth}{2} %%where n is the level,
-% starting with 0 (chapters only)
-% \usepackage{makeidx}
-% \makeindex 
-% \newcommand{\keyword}[1]{\textit{#1}\index{#1}} 
-%%%% this one adds the keyword 
-% %command: an italic emphasize and addition to the index.
-% \newcommand{\matlab}[1]{\texttt{#1}} %%%% this one adds the keyword 
-% 
-% 
-% \usepackage{geometry}
-% \geometry{inner=4.5cm} \geometry{outer=4cm}
-% \geometry{top=0.6cm} \geometry{bottom=9cm}
-% 
-% \begin{document}
+\documentclass[a4paper,10pt]{extreport}
+\usepackage{amssymb,amsfonts,amsmath,cite,enumerate}
+\setcounter{tocdepth}{2} %%where n is the level,starting with 0 (chapters only)
+\usepackage{makeidx}
+\makeindex 
+\newcommand{\keyword}[1]{\textit{#1}\index{#1}} 
+%%% this one adds the keyword 
+%command: an italic emphasize and addition to the index.
+\newcommand{\matlab}[1]{\texttt{#1}} %%%% this one adds the keyword 
+
+
+\usepackage{geometry}
+\geometry{inner=4.5cm} \geometry{outer=4cm}
+\geometry{top=0.6cm} \geometry{bottom=9cm}
+
+\begin{document}
 
 
 \chapter{Appendix: Basic Matrix Properties}
 
 
 
-\subsection{Skeel condition number [TBD]}
-% The Skeel condition number of a matrix A is less than or equal to ?(A) and it can be much smaller. I
-% 
-% 
-% % http://books.google.com.au/books?id=xi5omWiQ-3kC&pg=PA180&lpg=PA180&dq=skeel+condition+number&source=bl&ots=KjURfxXwca&sig=3TO9CeKv4WZNI3JlMk2565DrVyk&hl=en&sa=X&ei=_kcnUMKqOY-diAen_4Ao&ved=0CGQQ6AEwAQ#v=onepage&q=skeel%20condition%20number&f=false
-% 
-% http://books.google.com.au/books?id=31m4ahn_KfkC&pg=PA113&lpg=PA113&dq=skeel+condition+number&source=bl&ots=MKYWRDys8E&sig=jKcuFcEOUWvKOoezxX79HVHkAk4&hl=en&sa=X&ei=_kcnUMKqOY-diAen_4Ao&ved=0CJQBEOgBMBM#v=onepage&q=skeel%20condition%20number&f=false
+\subsection{Skeel condition number}
+Define\cite{watkins2002fundamentals} the Skeel condition number of A as:
 
-% Numerical Mathematics - Google Books Result
-% books.google.com.au/books?isbn=3540346589...Alfio Quarteroni, Riccardo Sacco, Fausto Saleri - 2007 - Mathematics - 655 pages
-% Remark 3.7 (The Skeel condition number) The Skeel condition number, defined as cond(A) = |A?1||A| ?, is the supremum over the set x? Rn, with x=0, of the ...
+$$
+skeel(A) = ||  |A^{-1}|\cdot |A|  ||_{\infty}
+$$
 
+Skeel condition number is usualy determined by iterative procedure. Skeel condition number is insensitive to row scaling, so it remains small while the normwise condition number $\kappa_\infty (A) $ becomes large in proportion to the badness of the sacling. 
 
+For further information, see\cite{skeel1980iterative} about the general definittion of Skeel numebr and\cite{higham1996accuracy} about the inexpensive methods of estimationg of skeel(A).
 
-% 
-% \bibliographystyle{unsrt}  \bibliography{biblio/kmvlinalgdecompose}
-% \printindex
-% \end{document}
+
+
+
+
+
+
+\bibliographystyle{unsrt}  \bibliography{biblio/kmvlinalgdecompose}
+\printindex
+\end{document}
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