Topics on Numerical Linear Algebra and High-Performance Computing
- 2009年3月25日（水） 13時30分-17時15分
- 京都大学グローバルCOE 知識循環社会のための情報学教育研究拠点
- IEEE関西支部 技術講演会
Taro Konda and Yoshimasa Nakamura (Kyoto University)
Introduction to New SVD Algorithms
Two new bidiagonal Singular Value Decomposition (SVD) algorithm are reviewed. One is the I-SVD algorithm which is a combination of the mdLVs algorithm and a twisted factorization of dLV type.
The other is the dDC algorithm of a simplified D&C and the dLV twist. The parallel dDC is also discussed. Comparisons with DBDSQR and DBDSDC of LAPACK and with PDBDSQR of ScaLAPACK are made.
Kinji Kimura, Takumi Yamashita and Yoshimasa Nakamura (Kyoto University)
The mdLVs algorithm using the generalized Newton bound as a shift of origin for computation of singular values
We discuss accuracy of the mdLVs algorithm for computing singular values of bidiagonal matrices using the generalized Newton shift.
The generalized Newton shift can be computed by simple recurrence relations. It is shown that the mdLVs with the generalized Newton shift achieves a higher relative accuracy than DLASQ routine of LAPACK which is based on the dqds algorithm with aggressive shift.
Julien Langou (University of Colorado, Denver)
Mixed single-double precision solver.
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach is based on standard iterative methods technique runned in 64-bit precision and preconditionned with a 32-bit factorization.
Julie Langou (University of Tennessee, Knoxville)
Past, present and future of the LAPACK library.
The LAPACK library dates back to 1992. Its interface is a de-facto standard for sequential linear algebra operations, its reference implementation (available on netlib) is widely used and provides a starting development point for most optimized version of the library. Indeed, on a wide range of functionalities, the reference implementation is as performant as optimized libraries. Since its creation, LAPACK aims at incorporating the latest state-of-the-art numerical linear algebra algorithms in a timely fashion and has been widely supported in that respect by the numerical linear algebra research community.
In this talk, we will recall the initial motivation for the creation of the LAPACK library and give some of the reasons for the success of the library. We will provide a comprehensive survey of the recent additions and modifications to the library since 2006. LAPACK has been designed for sequential computers with a hierarchy of caches. With the advent of multicore computers and the appeal of GPU computing, there is a need for new linear algebra libraries. We will stress the limitation of the LAPACK paradigm on these architectures and provide a quick overlook of PLASMA which is a software library designed to overcome these challenges. We will conclude by arguing for the need of a well-maintained reference implementation of the LAPACK library.