BibSonomyburst/user/ejr/ieee754BibSonomy RSS feed for /user/ejr/ieee7542012-02-16T02:00:21+01:00http://www.bibsonomy.org/bibtex/240d93f2b40efad3c754aef07c5c3dc08/ejrejr2007-10-09T07:04:05+02:00floatingpoint ieee754 <span class="authorEditorList"><a href="/author/Bindel">David Bindel</a>, and <a href="/author/Riedy">E. Jason Riedy</a> </span><em>IEEE-754r revision meeting, </em>(<em>August 2002</em>)Tue Oct 09 07:04:05 CEST 2007IEEE-754r revision meetingAugustException Handling Interfaces, Implementations, and Evaluation2002floatingpoint ieee754 http://www.bibsonomy.org/bibtex/2d9acf137472c48cd39527976dd61696d/ejrejr2007-10-09T07:04:05+02:00floatingpoint ieee754 <span class="authorEditorList"><a href="/author/Riedy">E. Jason Riedy</a> </span><em>ARITH&#039;05, </em>(<em>2005</em>)Tue Oct 09 07:04:05 CEST 2007{ARITH}'05Modern Language Tools and {754R}2005floatingpoint ieee754 http://www.bibsonomy.org/bibtex/2cdded1a468730acebe1a5b72cd540dd8/ejrejr2007-10-09T07:02:59+02:00eigenvalue floatingpoint ieee754 lapack lawn <span class="authorEditorList"><a href="/author/Marques">Osni A. Marques</a>, <a href="/author/Riedy">E. Jason Riedy</a>, and <a href="/author/Vömel">Christof Vömel</a> </span><em>LAPACK Working Note, </em><em>172. </em><em>Netlib, </em>(<em>September 2005</em>)Tue Oct 09 07:02:59 CEST 2007SeptemberAlso issued as UCB//CSD-05-1414; expanded from SISC version172Benefits of IEEE-754 Features in Modern Symmetric Tridiagonal EigensolversLAPACK Working Note2005eigenvalue floatingpoint ieee754 lapack lawn http://www.bibsonomy.org/bibtex/2c4c16874ca7686a01174ba4b107220f4/ejrejr2007-10-09T06:59:39+02:00floatingpoint ieee754 <span class="authorEditorList"><a href="/author/Hough">David Hough</a>, <a href="/author/Hay">Bill Hay</a>, <a href="/author/Kidder">Jeff Kidder</a>, <a href="/author/Riedy">E. Jason Riedy</a>, <a href="/author/Jr.">Guy L. Steele Jr.</a>, and <a href="/author/Thomas">Jim Thomas</a> </span><em>17th IEEE Symposium on Computer Arithmetic ARITH&#039;05, </em>(<em>2005</em>)Tue Oct 09 06:59:39 CEST 200717th IEEE Symposium on Computer Arithmetic (ARITH'05)Arithmetic Interactions: From Hardware to Applications2005floatingpoint ieee754 The entire process of creating and executing applications that solve interesting problems with acceptable cost and accuracy involves a complex interaction among hardware, system software, programming environments, mathematical software libraries, and applications software, all mediated by standards for arithmetic, operating systems, and programming environments. This panel will discuss various issues arising among these various contending points of view, sometimes from the point of view of issues raised during the current IEEE 754R standards revision effort.http://www.bibsonomy.org/bibtex/22b60b413d9447d55594c945679fdb1dd/ejrejr2007-10-09T06:57:00+02:00eigenvalue floatingpoint ieee754 siam sisc <span class="authorEditorList"><a href="/author/Marques">Osni A. Marques</a>, <a href="/author/Riedy">E. Jason Riedy</a>, and <a href="/author/Vömel">Christof Vömel</a> </span><em>SIAM Journal on Scientific Computing</em> <em>28(5):1613--1633</em> (<em>2006</em>)Tue Oct 09 06:57:00 CEST 2007SIAM Journal on Scientific Computing51613--1633Benefits of {IEEE-754} Features in Modern Symmetric Tridiagonal Eigensolvers282006eigenvalue floatingpoint ieee754 siam sisc Bisection is one of the most common methods used to compute the eigenvalues of symmetric tridiagonal matrices. Bisection relies on the Sturm count: For a given shift sigma, the number of negative pivots in the factorization $T - \sigma I = LDL^T$ equals the number of eigenvalues of T that are smaller than sigma. In IEEE-754 arithmetic, the value $\infty$ permits the computation to continue past a zero pivot, producing a correct Sturm count when $T$ is unreduced. Demmel and Li showed [IEEE Trans. Comput., 43 (1994), pp. 983–992] that using $\infty$ rather than testing for zero pivots within the loop could significantly improve performance on certain architectures. When eigenvalues are to be computed to high relative accuracy, it is often preferable to work with $LDL^T$ factorizations instead of the original tridiagonal $T$. One important example is the MRRR algorithm. When bisection is applied to the factored matrix, the Sturm count is computed from $LDL^T$ which makes differential stationary and progressive qds algorithms the methods of choice. While it seems trivial to replace $T$ by $LDL^T$, in reality these algorithms are more complicated: In IEEE-754 arithmetic, a zero pivot produces an overflow followed by an invalid exception (NaN, or "Not a Number") that renders the Sturm count incorrect. We present alternative, safe formulations that are guaranteed to produce the correct result. Benchmarking these algorithms on a variety of platforms shows that the original formulation without tests is always faster provided that no exception occurs. The transforms see speed-ups of up to 2.6x over the careful formulations. Tests on industrial matrices show that encountering exceptions in practice is rare. This leads to the following design: First, compute the Sturm count by the fast but unsafe algorithm. Then, if an exception occurs, recompute the count by a safe, slower alternative. The new Sturm count algorithms improve the speed of bisection by up to 2x on our test matrices. Furthermore, unlike the traditional tiny-pivot substitution, proper use of IEEE-754 features provides a careful formulation that imposes no input range restrictions.