From 1483c7afd7fac42d8e35119ccfc958c455dcc05d Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Sun, 20 Mar 2016 00:46:40 -0400
Subject: [PATCH] books/bookvolbib Add Fern92 Accurate Singular Values
Goal: Axiom Numerics
@techreport{Fern92,
author = "Fernando, K. Vince and Parlett, Beresford N.",
title = "Accurate Singular Values and Differential qd Algorithms",
year = "1992",
institution = "University of California, Berkeley",
type = "Technical Report",
number = "PAM-554",
paper = "Fern92.pdf",
url = "http://www.dtic.mil/dtic/tr/fulltext/u2/a256582.pdf",
abstract =
"We have discovered a new implementaiton of the qd algorithm that has
a far wider domain of stability than Rutishauser's version. Our
algorithm was developed from an examination of the LR-Cholesky
transformation and can be adapted to parallel computation in stark
contrast to traditional qd. Our algorithm also yields useful a
posteriori upper and lower bounds on the smallest singular value of a
bidiagonal matrix.
The zero-shift bidiagonal QR of Demmel and Kahan computes the smallest
singlar values to maximal relative accuracy and the others to maximal
absolute accuracy with little or no degradation in efficiency when
compared with the LINPACK code. Our algorithm obtains maximal relative
accuracy for all the singluar values and runs at least four times
faster than the LINPACK code."
}
---
books/bookvolbib.pamphlet | 31 ++++++++++++++++++++++++++++
changelog | 2 +
patch | 43 +++++++++++++++++++++------------------
src/axiom-website/patches.html | 2 +
4 files changed, 58 insertions(+), 20 deletions(-)
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 2352e8e..7156519 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -1974,6 +1974,37 @@ when shown in factored form.
\end{chunk}
+\index{Fernando, K. Vince}
+\index{Parlett, Beresford N.}
+\begin{chunk}{axiom.bib}
+@techreport{Fern92,
+ author = "Fernando, K. Vince and Parlett, Beresford N.",
+ title = "Accurate Singular Values and Differential qd Algorithms",
+ year = "1992",
+ institution = "University of California, Berkeley",
+ type = "Technical Report",
+ number = "PAM-554",
+ paper = "Fern92.pdf",
+ url = "http://www.dtic.mil/dtic/tr/fulltext/u2/a256582.pdf",
+ abstract =
+ "We have discovered a new implementaiton of the qd algorithm that has
+ a far wider domain of stability than Rutishauser's version. Our
+ algorithm was developed from an examination of the LR-Cholesky
+ transformation and can be adapted to parallel computation in stark
+ contrast to traditional qd. Our algorithm also yields useful a
+ posteriori upper and lower bounds on the smallest singular value of a
+ bidiagonal matrix.
+
+ The zero-shift bidiagonal QR of Demmel and Kahan computes the smallest
+ singlar values to maximal relative accuracy and the others to maximal
+ absolute accuracy with little or no degradation in efficiency when
+ compared with the LINPACK code. Our algorithm obtains maximal relative
+ accuracy for all the singluar values and runs at least four times
+ faster than the LINPACK code."
+}
+
+\end{chunk}
+
\index{Kelsey, Tom}
\begin{chunk}{ignore}
{Kel00,
diff --git a/changelog b/changelog
index 42189be..ce5bcda 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20160320 tpd src/axiom-website/patches.html 20160320.03.tpd.patch
+20160320 tpd books/bookvolbib Add Fern92 Accurate Singular Values
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
diff --git a/patch b/patch
index f899ed9..e14b1c8 100644
--- a/patch
+++ b/patch
@@ -1,26 +1,29 @@
-books/bookvolbib Add Demm88 Computing Small Singular Values
+books/bookvolbib Add Fern92 Accurate 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",
+@techreport{Fern92,
+ author = "Fernando, K. Vince and Parlett, Beresford N.",
+ title = "Accurate Singular Values and Differential qd Algorithms",
+ year = "1992",
+ institution = "University of California, Berkeley",
type = "Technical Report",
- number = "326",
- paper = "Demm88.pdf",
+ number = "PAM-554",
+ paper = "Fern92.pdf",
+ url = "http://www.dtic.mil/dtic/tr/fulltext/u2/a256582.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."
+ "We have discovered a new implementaiton of the qd algorithm that has
+ a far wider domain of stability than Rutishauser's version. Our
+ algorithm was developed from an examination of the LR-Cholesky
+ transformation and can be adapted to parallel computation in stark
+ contrast to traditional qd. Our algorithm also yields useful a
+ posteriori upper and lower bounds on the smallest singular value of a
+ bidiagonal matrix.
+
+ The zero-shift bidiagonal QR of Demmel and Kahan computes the smallest
+ singlar values to maximal relative accuracy and the others to maximal
+ absolute accuracy with little or no degradation in efficiency when
+ compared with the LINPACK code. Our algorithm obtains maximal relative
+ accuracy for all the singluar values and runs at least four times
+ faster than the LINPACK code."
}
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 2c633da..677da42 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5240,6 +5240,8 @@ books/bookvolbib Add Nguy16 on Higher-order symbolic execution

books/bookvolbib Sutt13, Computing the Complete CS Decomposition

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

+20160320.03.tpd.patch
+books/bookvolbib Add Fern92 Accurate Singular Values

--
1.7.5.4