**Upcoming Events**

Monday, March 6, 2017 at 3:00 PM in SAS 4201

Takeshi Ogita , Tokyo Womans Christian University

Takeshi Ogita , Tokyo Womans Christian University

A preconditioning method for dense linear systems

This talk is concerned with accurate numerical solutions

of ill-conditioned dense linear systems. Recently, we have

developed some preconditioning methods for this purpose.

Using such preconditioned methods, the condition number

of the coefficient matrices can be reduced sufficiently.

However, computational cost for such a preconditioning is

considerably larger than the standard numerical algorithm

such as LU factorization, since high-precision matrix

multiplication is required. In this talk, we modify this

point by exploiting the structure of the coefficient

matrix and develop an efficient algorithm for solving

ill-conditioned linear systems in high accuracy.

As a result, computational cost for preconditioning can

be significantly reduced with similar quality to the

previous methods. Numerical results are presented

showing the performance of the algorithm.

Monday, March 6, 2017 at 3:30 PM in SAS 4201

Siegfried M. Rump, Hamburg Technical University and Waseda University, Tokyo

Siegfried M. Rump, Hamburg Technical University and Waseda University, Tokyo

Reproducible summation, error-free transformations, and floating-point error estimates

Recently, reproducible summation gained much interest. The main problem is the lack of associativity of floating-point addition. One possibility to attack the problem is to compute without error, for example using error-free transformations. Some algorithms to that end will be presented. In a second part we will show new and improved error estimates for floating-point summation. As a new result, we completely refrain from using some floating-point grid. In contrast, we treat perturbed real sums, i.e., each individual addition is somehow perturbed, where there is almost no restriction on the size or kind of the perturbations. Nevertheless, we can avoid higher order terms in the error estimates.

Tuesday, March 14, 2017 at 3:00 PM in SAS 4201

Dirk Lorenz, TU Braunschweig

Dirk Lorenz, TU Braunschweig

TBA

TBA

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Seminar Organizers: A. Alexanderian, A. Saibab, D. Papp