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

本项目在多核CPU环境下的并行计算中获得了以下成果。1)提出了一种基于广义牛顿位移的mdlv计算双对角奇异值的移位策略。2)利用Householder变换和紧凑的WY表示，提高了奇异向量再正交化的速度。3)将预处理过程从给定的密集矩阵加速到双对角矩阵。4)讨论了GPGPU双精度计算中I-SVD和D & C等奇异值分解算法的性能和精度评价。5)设计了计算一类带矩阵特征值和奇异值的可积算法。快速I-SVD算法在1)-4)方面的结果代码DBDSLV可以在网页上下载，并且在国际研讨会和年度会议上做了许多报告，并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.