From 4a23046a974fefe667e36bec0a553203c58f91f3 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Sun, 20 Mar 2016 00:27:47 -0400
Subject: [PATCH] books/bookvolbib Add Demm88 Computing Small Singular Values
Goal: Axiom Numerics
@techreport{Demm88,
author = "Demmel, James and Kahan, W.",
title = "Computing Small Singular Values of Bidiagonal Matrices with
Guaranteed High Relative Accuracy",
year = "1988",
institution = "New York University",
type = "Technical Report",
number = "326",
paper = "Demm88.pdf",
abstract =
"Computing the singular values of a bidiagonal matrix is the final
phase of the standard algorithm for the singular value decomposition
of a general matrix. We present a new algorithm which computes all the
singular values of a bidiagonal matrix to high relative accuracy
independent of their magnitudes. In contrast, the standard algorithm
for bidiagonal matrices may compute small singular values with no
relative accuracy at all. Numerical experiments show that the new
algorithm is comparable in speed to the standard algorithm, and
frequently faster. We also show how to accurately compute tiny
eigenvalues of some classes of symmetric trigiagonal matrices using
the same technique."
}
---
books/bookvolbib.pamphlet | 28 ++++++++++++++++++++++++++
changelog | 2 +
patch | 43 +++++++++++++++++++--------------------
src/axiom-website/patches.html | 2 +
4 files changed, 53 insertions(+), 22 deletions(-)
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 2336d54..2352e8e 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -1906,6 +1906,34 @@ when shown in factored form.
\end{chunk}
+\index{Demmel, James}
+\index{Kahan, W.}
+\begin{chunk}{axiom.bib}
+@techreport{Demm88,
+ author = "Demmel, James and Kahan, W.",
+ title = "Computing Small Singular Values of Bidiagonal Matrices with
+ Guaranteed High Relative Accuracy",
+ year = "1988",
+ institution = "New York University",
+ type = "Technical Report",
+ number = "326",
+ paper = "Demm88.pdf",
+ abstract =
+ "Computing the singular values of a bidiagonal matrix is the final
+ phase of the standard algorithm for the singular value decomposition
+ of a general matrix. We present a new algorithm which computes all the
+ singular values of a bidiagonal matrix to high relative accuracy
+ independent of their magnitudes. In contrast, the standard algorithm
+ for bidiagonal matrices may compute small singular values with no
+ relative accuracy at all. Numerical experiments show that the new
+ algorithm is comparable in speed to the standard algorithm, and
+ frequently faster. We also show how to accurately compute tiny
+ eigenvalues of some classes of symmetric trigiagonal matrices using
+ the same technique."
+}
+
+\end{chunk}
+
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate13,
diff --git a/changelog b/changelog
index 8e1e5b8..42189be 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20160320 tpd src/axiom-website/patches.html 20160320.02.tpd.patch
+20160320 tpd books/bookvolbib Add Demm88 Computing Small Singular Values
20160320 tpd src/axiom-website/patches.html 20160320.01.tpd.patch
20160320 tpd books/bookvolbib Sutt13, Computing the Complete CS Decomposition
20160319 tpd src/axiom-website/patches.html 20160319.05.tpd.patch
diff --git a/patch b/patch
index 545c3ac..f899ed9 100644
--- a/patch
+++ b/patch
@@ -1,27 +1,26 @@
-books/bookvolbib Add Sutt13, Computing the Complete CS Decomposition
+books/bookvolbib Add Demm88 Computing Small Singular Values
Goal: Axiom Numerics
-@article{Sutt13,
- author = "Sutton, Brian D.",
- title = "Computing the Complete CS Decomposition",
- year = "2013",
- month = "February",
- url = "http://arxiv.org/pdf/0707.1838v3.pdf",
- paper = "Sutt13.pdf",
+@techreport{Demm88,
+ author = "Demmel, James and Kahan, W.",
+ title = "Computing Small Singular Values of Bidiagonal Matrices with
+ Guaranteed High Relative Accuracy",
+ year = "1988",
+ institution = "New York University",
+ type = "Technical Report",
+ number = "326",
+ paper = "Demm88.pdf",
abstract =
- "An algorithm is developed to compute the complete CS decomposition
- (CSD) of a partitioned unitary matrix. Although the existence of the
- CSD has been recognized since 1977, prior algorithms compute only a
- reduced version (the 2-by-1 CSD) that is equivalent to two
- simultaneous singular value decompositions. The algorithm presented
- here computes the complete 2-by-2 CSD, which requires the simultaneous
- diagonalization of all four blocks of a unitary matrix partitioned
- into a 2-by-2 block structure. The algorithm appears to be the only
- fully specified algorithm available. The computation occurs in two
- phases. In the first phase, the unitary matrix is reduced to
- bidiagonal block form, as described by Sutton and Edelman. In the
- second phase, the blocks are simultaneously diagonalized using
- techniques from bidiagonal SVD algorithms of Golub, Kahan, and
- Demmel. The algorithm has a number of desirable numerical features."
+ "Computing the singular values of a bidiagonal matrix is the final
+ phase of the standard algorithm for the singular value decomposition
+ of a general matrix. We present a new algorithm which computes all the
+ singular values of a bidiagonal matrix to high relative accuracy
+ independent of their magnitudes. In contrast, the standard algorithm
+ for bidiagonal matrices may compute small singular values with no
+ relative accuracy at all. Numerical experiments show that the new
+ algorithm is comparable in speed to the standard algorithm, and
+ frequently faster. We also show how to accurately compute tiny
+ eigenvalues of some classes of symmetric trigiagonal matrices using
+ the same technique."
}
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index c291a37..2c633da 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5238,6 +5238,8 @@ books/bookvol10.5 update BLAS to 3.6.0 with lisp code

books/bookvolbib Add Nguy16 on Higher-order symbolic execution

20160320.01.tpd.patch
books/bookvolbib Sutt13, Computing the Complete CS Decomposition

+20160320.02.tpd.patch
+books/bookvolbib Add Demm88 Computing Small Singular Values

--
1.7.5.4