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Detalji o izabranom predavanju:
| Seminar: | Seminar za numeričku matematiku i znan. računanje |
| Naziv predavanja: | Error analysis and parallelization technique of the one-sided Jacobi method with blocking |
| Predavač: | Shuhei Kudo |
| Vrijeme: |
08.03.2018 12:15 |
| Predavaonica: | 104 |
| Tip: |
Gost seminara |
| Opis: | In this talk, we will focus on the accuracy and parallel implementation of the one-sided Jacobi method (OSJ) with blocking. OSJ is a method for computing the singular value decomposition (SVD) of dense matrices, which is superior to the bi-diagonalization based methods in terms of accuracy and inherent parallelism. The blocking technique can improve the performance of OSJ, but changes its mathematical and numerical properties, making the convergence of the method in floating-point arithmetic difficult to analyze.
In the first part of this talk, we analyze the rounding error of a blocking method for OSJ called “V2”. Our analysis using the column scaling structure of the input matrix gives a better upper bound on the orthogonality error of the V2 method than the previous analysis and explains why the V2 method converges in practice.
In the second part, we will describe our parallelization technique of OSJ with the V2 method. Our technique utilizes both parallelism in OSJ and V2 method to reduce the number of communication while keeping the order computation the same. Performance results of our implementation on a massively-parallel super computer are also presented. |
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