| Popis: |
The problem of tradeoff between accuracy and efficiency is one of the core problems in matrix computations software development. More accurate algorithms are usually less efficient than less accurate but much faster algorithms. In the case of SVD, it is known that the one--sided Jacobi algorithm is more accurate but much slower than the methods based on bidiagonalization (such as the QR and the divide and conquer method). On the other hand, the one--sided Jacobi algorithm is perfect for parallelization and it has been studied by many researches. Many parallel strategies and other techniques are developed to improve the performance of the Jacobi algorithm in parallel environment. The focus of our talk are new results regarding the convergence behavior of a modified Jacobi SVD algorithm. In our opinion, this new implementation of the Jacobi algorithm, with swift numerical convergence, will require new techniques for efficient parallelization. |
