S.M.Rump氏 (Hamburg-Harburg大学教授)講演会
場所 早稲田大学理工学部51号館3階第3会議室(新宿区大久保3-4-1)
精度保証付き数値計算の話題I
日時 10月22日(月) 2:40-4:10
精度保証付き数値計算の話題I
日時 10月24日(水) 2:40-4:10
Rump氏は精度保証付き数値計算の研究分野に長く従事し，さまざまな理論やMATLAB上のTool Box INTLABの開発などで良い成果を出されています。本分野の入門から初めて，対称性のある摂動の理論など氏の最新成果まで２回にわたり講演いただきます。皆様のご参加をお待ちしております。
次の国際ワークショップを開催します。参加自由，無料ですので奮ってご参加いただければ幸いです。
International Workshop on Numerical Analysis with Guaranteed Accuracy
Oct. 8 13:00-18:10
The Third Meeting Room, 51-Building, School of Science and Engineering, Waseda University, Tokyo 169-8555
Sponsored by Waseda University, IEICE, Technical Group on Self-Validating Computing Japan Society for Simulation Technology, Japan SIAM
Program: 8 Oct
(1) 13:00-13:50 Gotz Alefeld(Universitat Karlsruhe) Verification of solutions of linear and nonlinear complementarity problems
(2) 13:50-14:30 Markus Neher(Universitat Karlsruhe) Geometric Series Bounds for the Local Errors of Taylor Methods for ODEs
(3) 14:40-15:30 Jurgen P. Herzberger (Universitaet Oldenburg) Bounds for the effective rate of interest of some special cashflows
Abstrct: We first consider the cashflow of an ordinary simple annuity. Applying the principles in finance and the US-rule for the calculation of the effective rate of interest, we get as result a certain polynomial to be solved for its unique positive root. Under closer inspection, this type of polynomial has already been considered in Numerical Analysis in connection with the calculation of the $Q$-order or $R$-order of convergence of iterative numerical processes, beginning with A.~Ostrowski and J.F.~Traub. It can be shown that the bounds for the positive root in question in some later papers can indeed easily be derived by applying a simple variable transformation to such a polynomial and to the bounds given by J.F.~Traub. Next, we examine an interesting practical problem concerning the estimation or the bounding of the effective rate of interest of an annuity which we get by changing in a certain way the conditions of a given annuity with known datas. We give quite reasonable bounds for the effective rate of the changed annuities in terms of the effective rate of the original one. This question will then be reconsidered under the more general aspect of an annuity with geometrically growing payments. Applying the results of the first part of the talk we get also bounds in this case in a simple manner. As a kind of byproduct we show an interesting possibility for bounding the order of convergence of certain types of interpolatory iteration methods in Numerical Analysis and thus come back to the oberservation at the beginning.
(4) 15:30-16:00 Wolfgang Schwarz (Technische Universitaet Dresden) Some open problems form chaos theory
(5) 16:10-16:40 Yusuke Nakaya (Waseda Univ) Fast implementation of Krawczyk's method
(6) 16:40-17:10 Maruyama (Waseda Univ) Element-wise eigenvalue inclusion method
(7) 17:10-17:40 Shin'ichi Oishi (Waseda Univ) Slab: a MATLAB-like interpreter for verified computation
(8) 17:30-18:10 Lylia A'tanassova(MAN,Munich) Convex directions for complex Hurwitz stable polynomials and quasipolynomials