From 5c831f94f1a81e9b1232e7cc4ce77f9aef37be22 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Sat, 26 Mar 2016 17:13:31 -0400
Subject: [PATCH] books/bookvolbib Demm08 Householder QR
Goal: Axiom Literate Programming
@techreport{Demm08,
author = "Demmel, James and Hoemmen, Mark and Hida, Yozo
and Riedy, E. Jason",
title = "Non-Negative Diagonals and High Performance on Low-Profile
Matrices from Householder QR",
year = "2008",
institution = "Univerity of California, Berkeley",
type = "Technical Report",
number = "203",
paper = "Demm08.pdf",
url = "http://www.netlib.org/lapack/lawnspdf/lawn203.pdf",
abstract =
"The Householder reflections used in LAPACK's QR factorization leave
positive and negative real entries along R's diagonal. This is
sufficient for most applications of QR factorizations, but a few
require that R have a non-negative diagonal. This note provides a new
Householder generation routine to produce a non-negative
diagonal. Additionally, we find that scanning for trailing zeros in
the generated reflections leads to large performance improvements when
applying reflections with many trailing zeros. Factoring low-profile
matrices, those with non-zero entries mostly near the diagonal (e.g
band matrices), now requires far fewer operations. For example, QR
factorization of matrices with profile width $b$ that are stored
densely in an $n \cross n$ matrix improves form $O(n^3)$ to $O(n^2+nb^2)$."
---
books/bookvolbib.pamphlet | 33 +++++++++++++++++++++++++++++++++
changelog | 2 ++
patch | 28 ++++++++++++++++++++++++++--
src/axiom-website/patches.html | 2 ++
4 files changed, 63 insertions(+), 2 deletions(-)
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index bfcc2bc..96e5259 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -1979,6 +1979,39 @@ when shown in factored form.
\end{chunk}
+\index{Demmel, James W.}
+\index{Hoemmen, Mark}
+\index{Hida, Yozo}
+\index{Riedy, E. Jason}
+\begin{chunk}{axiom.bib}
+@techreport{Demm08,
+ author = "Demmel, James and Hoemmen, Mark and Hida, Yozo
+ and Riedy, E. Jason",
+ title = "Non-Negative Diagonals and High Performance on Low-Profile
+ Matrices from Householder QR",
+ year = "2008",
+ institution = "Univerity of California, Berkeley",
+ type = "Technical Report",
+ number = "203",
+ paper = "Demm08.pdf",
+ url = "http://www.netlib.org/lapack/lawnspdf/lawn203.pdf",
+ abstract =
+ "The Householder reflections used in LAPACK's QR factorization leave
+ positive and negative real entries along R's diagonal. This is
+ sufficient for most applications of QR factorizations, but a few
+ require that R have a non-negative diagonal. This note provides a new
+ Householder generation routine to produce a non-negative
+ diagonal. Additionally, we find that scanning for trailing zeros in
+ the generated reflections leads to large performance improvements when
+ applying reflections with many trailing zeros. Factoring low-profile
+ matrices, those with non-zero entries mostly near the diagonal (e.g
+ band matrices), now requires far fewer operations. For example, QR
+ factorization of matrices with profile width $b$ that are stored
+ densely in an $n \cross n$ matrix improves form $O(n^3)$ to $O(n^2+nb^2)$."
+}
+
+\end{chunk}
+
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate13,
diff --git a/changelog b/changelog
index 49acc2b..4663256 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20160326 tpd src/axiom-website/patches.html 20160326.01.tpd.patch
+20160326 tpd books/bookvolbib Demm08 Householder QR
20160325 tpd src/axiom-website/patches.html 20160325.04.tpd.patch
20160325 tpd src/input/Makefile add groeb2.input
20160325 tpd src/input/groeb2.input Demonstrate Groebner basis
diff --git a/patch b/patch
index 54328fa..ad5e115 100644
--- a/patch
+++ b/patch
@@ -1,4 +1,28 @@
-src/input/groeb2.input Demonstrate Groebner basis
+books/bookvolbib Demm08 Householder QR
-Goal: Axiom Algebra
+Goal: Axiom Literate Programming
+@techreport{Demm08,
+ author = "Demmel, James and Hoemmen, Mark and Hida, Yozo
+ and Riedy, E. Jason",
+ title = "Non-Negative Diagonals and High Performance on Low-Profile
+ Matrices from Householder QR",
+ year = "2008",
+ institution = "Univerity of California, Berkeley",
+ type = "Technical Report",
+ number = "203",
+ paper = "Demm08.pdf",
+ url = "http://www.netlib.org/lapack/lawnspdf/lawn203.pdf",
+ abstract =
+ "The Householder reflections used in LAPACK's QR factorization leave
+ positive and negative real entries along R's diagonal. This is
+ sufficient for most applications of QR factorizations, but a few
+ require that R have a non-negative diagonal. This note provides a new
+ Householder generation routine to produce a non-negative
+ diagonal. Additionally, we find that scanning for trailing zeros in
+ the generated reflections leads to large performance improvements when
+ applying reflections with many trailing zeros. Factoring low-profile
+ matrices, those with non-zero entries mostly near the diagonal (e.g
+ band matrices), now requires far fewer operations. For example, QR
+ factorization of matrices with profile width $b$ that are stored
+ densely in an $n \cross n$ matrix improves form $O(n^3)$ to $O(n^2+nb^2)$."
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 397e2fd..27c15f0 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5256,6 +5256,8 @@ books/bookvol10.2.pamphlet add zero? to MATRIX

books/bookvolbib add Demm05 LAPACK Working Note 165

20160325.04.tpd.patch
src/input/groeb2.input Demonstrate Groebner basis

+20160326.01.tpd.patch
+books/bookvolbib Demm08 Householder QR

--
1.7.5.4