From 3f9cf0a76f797a6f296ba537fc9e6b038588ecd8 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Fri, 25 Mar 2016 19:18:07 0400
Subject: [PATCH] books/bookvolbib add Demm05 LAPACK Working Note 165
Goal: Axiom Literate Programming
@techreport{Demm05,
author = "Demmel, James and Hida, Yozo and Kahan, W. and Li, Xiaoye S.
and Mukherjee, Soni and Riedy, E. Jason",
title = "Error Bounds from Extra Precise Iterative Refinement",
year = "2005",
institution = "Univerity of California, Berkeley",
type = "Technical Report",
number = "165",
paper = "Demm05.pdf",
url = "http://www.netlib.org/lapack/lawnspdf/lawn165.pdf",
abstract =
"We present the design and testing of an algorithm for iterative
refinement of the solution of linear equations, were the residual is
computed with extra precision. This algorithm was originally proposed
in the 1960s as a means to compute very accurate solutions to all but
the most illconditioned linear systems of equations. However two
obstacles hae until now prevented its adoption in standard subroutine
libraries like LAPACK: (1) There was no standard way to access the
higher precision arithmetic needed to compute residuals, and (2) it
was unclear how to compute a reliable error bound for the computed
solution. The completion of the new BLAS Technical Forum Standard has
recently removed the first obstacle. To overcome the second obstacle,
we show how a single application of iterative refindment can be used
to copute an error bound in any norm at small cost, and use this to
compute both an error bound in the usual infinity norm, and a
componentwise relative error bound.
We report extensive test results on over 6.2 million matrices of
dimension 5, 10, 100, and 1000. As long as a normwise
(resp. componentwise) condition number computed by the algorithm is
less than $1/max(10,\sqrt{n})\epsilon_w$, the computed normwise
(resp. componentwise) error bound is at most
$2max(10,\sqrt{n})\epsilon_w$, and indeed bounds the true error. Here,
$n$ is the matrix dimension and $\epsilon_w$ is a single precision
roundoff error. For worse conditioned problems, we get similarly small
correct error bounds in over 89.4\% of cases."
}

books/bookvolbib.pamphlet  54 ++++++++++++++++++++++++++++++++++
changelog  2 +
patch  42 +++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 91 insertions(+), 9 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 2450594..bfcc2bc 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 18,8 +18,6 @@ named algorithm or author.
Introduction of special terms (e.g. Toeplitz matrix) may include a
paragraph for those unfamiliar with the terms.
\chapter{The Bibliography}

\section{Algebra Documentation References}
\index{Gonshor, H.}
@@ 1934,6 +1932,53 @@ when shown in factored form.
\end{chunk}
+\index{Demmel, James}
+\index{Hida, Yozo}
+\index{Kahan, W.}
+\index{Li, Xiaoye S.}
+\index{Mukherjee, Soni}
+\index{Riedy, E. Jason}
+\begin{chunk}{axiom.bib}
+@techreport{Demm05,
+ author = "Demmel, James and Hida, Yozo and Kahan, W. and Li, Xiaoye S.
+ and Mukherjee, Soni and Riedy, E. Jason",
+ title = "Error Bounds from Extra Precise Iterative Refinement",
+ year = "2005",
+ institution = "Univerity of California, Berkeley",
+ type = "Technical Report",
+ number = "165",
+ paper = "Demm05.pdf",
+ url = "http://www.netlib.org/lapack/lawnspdf/lawn165.pdf",
+ abstract =
+ "We present the design and testing of an algorithm for iterative
+ refinement of the solution of linear equations, were the residual is
+ computed with extra precision. This algorithm was originally proposed
+ in the 1960s as a means to compute very accurate solutions to all but
+ the most illconditioned linear systems of equations. However two
+ obstacles hae until now prevented its adoption in standard subroutine
+ libraries like LAPACK: (1) There was no standard way to access the
+ higher precision arithmetic needed to compute residuals, and (2) it
+ was unclear how to compute a reliable error bound for the computed
+ solution. The completion of the new BLAS Technical Forum Standard has
+ recently removed the first obstacle. To overcome the second obstacle,
+ we show how a single application of iterative refindment can be used
+ to copute an error bound in any norm at small cost, and use this to
+ compute both an error bound in the usual infinity norm, and a
+ componentwise relative error bound.
+
+ We report extensive test results on over 6.2 million matrices of
+ dimension 5, 10, 100, and 1000. As long as a normwise
+ (resp. componentwise) condition number computed by the algorithm is
+ less than $1/max(10,\sqrt{n})\epsilon_w$, the computed normwise
+ (resp. componentwise) error bound is at most
+ $2max(10,\sqrt{n})\epsilon_w$, and indeed bounds the true error. Here,
+ $n$ is the matrix dimension and $\epsilon_w$ is a single precision
+ roundoff error. For worse conditioned problems, we get similarly small
+ correct error bounds in over 89.4\% of cases."
+}
+
+\end{chunk}
+
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate13,
@@ 17208,11 +17253,6 @@ Math. Tables Aids Comput. 10 9196. (1956)
\eject
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Bibliography}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\bibliographystyle{axiom}
\bibliography{axiom}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Index}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\printindex
diff git a/changelog b/changelog
index dc84fb2..064aa80 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160325 tpd src/axiomwebsite/patches.html 20160325.03.tpd.patch
+20160325 tpd books/bookvolbib add Demm05 LAPACK Working Note 165
20160325 tpd src/axiomwebsite/patches.html 20160325.02.tpd.patch
20160325 tpd books/bookvol10.2.pamphlet add zero? to MATRIX
20160325 tpd src/axiomwebsite/patches.html 20160325.01.tpd.patch
diff git a/patch b/patch
index 18a6740..16309f0 100644
 a/patch
+++ b/patch
@@ 1,3 +1,41 @@
books/bookvol10.2.pamphlet add zero? to MATRIX
+books/bookvolbib add Demm05 LAPACK Working Note 165
Goal: Axiom Algebra
+Goal: Axiom Literate Programming
+
+@techreport{Demm05,
+ author = "Demmel, James and Hida, Yozo and Kahan, W. and Li, Xiaoye S.
+ and Mukherjee, Soni and Riedy, E. Jason",
+ title = "Error Bounds from Extra Precise Iterative Refinement",
+ year = "2005",
+ institution = "Univerity of California, Berkeley",
+ type = "Technical Report",
+ number = "165",
+ paper = "Demm05.pdf",
+ url = "http://www.netlib.org/lapack/lawnspdf/lawn165.pdf",
+ abstract =
+ "We present the design and testing of an algorithm for iterative
+ refinement of the solution of linear equations, were the residual is
+ computed with extra precision. This algorithm was originally proposed
+ in the 1960s as a means to compute very accurate solutions to all but
+ the most illconditioned linear systems of equations. However two
+ obstacles hae until now prevented its adoption in standard subroutine
+ libraries like LAPACK: (1) There was no standard way to access the
+ higher precision arithmetic needed to compute residuals, and (2) it
+ was unclear how to compute a reliable error bound for the computed
+ solution. The completion of the new BLAS Technical Forum Standard has
+ recently removed the first obstacle. To overcome the second obstacle,
+ we show how a single application of iterative refindment can be used
+ to copute an error bound in any norm at small cost, and use this to
+ compute both an error bound in the usual infinity norm, and a
+ componentwise relative error bound.
+
+ We report extensive test results on over 6.2 million matrices of
+ dimension 5, 10, 100, and 1000. As long as a normwise
+ (resp. componentwise) condition number computed by the algorithm is
+ less than $1/max(10,\sqrt{n})\epsilon_w$, the computed normwise
+ (resp. componentwise) error bound is at most
+ $2max(10,\sqrt{n})\epsilon_w$, and indeed bounds the true error. Here,
+ $n$ is the matrix dimension and $\epsilon_w$ is a single precision
+ roundoff error. For worse conditioned problems, we get similarly small
+ correct error bounds in over 89.4\% of cases."
+}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 4315674..7ca5dc5 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5252,6 +5252,8 @@ books/bookvol13 Quote example Euclid proof using TLA+
license/license.lapack Add LAPACK license
20160325.02.tpd.patch
books/bookvol10.2.pamphlet add zero? to MATRIX
+20160325.03.tpd.patch
+books/bookvolbib add Demm05 LAPACK Working Note 165

1.7.5.4