Development of Innovative Library for Singular Value Decomposition Suited to Multi-Core Processors

本项目在多核CPU环境下的并行计算方面取得了以下成果。1)提出了一种基于广义牛顿移位的移位策略，用于mdLV计算双对角奇异值。2)本文利用Householder变换和紧WY表示，建立了奇异向量重正交化的加速方法。3)对给定稠密矩阵到双对角矩阵的预处理过程进行了加速。4)讨论了GPGPU双精度计算中奇异值分解算法I-SVD和D & C的性能和精度评价。5)设计了一类带矩阵特征值和奇异值的新的可积算法。根据1）-4）的快速I-SVD算法的结果代码DBDSLV可以在网页上下载，并且已经在国际研讨会和年会上进行了许多演示，并且已经发表了许多研究论文。

This project obtains the following fruits in parallel computations with multi-core CPU environments. 1) A shift strategy based on the generalized Newton shift is completed for computing bidiagonal singular values by the mdLVs. 2) A speed up is established in reorthogonalization of singular vectors by using the Householder transformation with the compact WY representation. 3) A speed up of preconditioning process from given dense matrix to bidiagonal is performed. 4) Evaluation both of performance and accuracy of some singular value decomposition algorithms including I-SVD and D & C in double precision computation in GPGPU are discussed. 5) New integrable algorithms for computing eigenvalues and singular values of some class of band matrices are designed. The resulting code DBDSLV of the fast I-SVD algorithm in terms of 1)-4) can be downloaded in the web page as well as many presentations have been given in international workshops and annual meetings and many research papers have been published.