計算の品質研究部会OSプログラム： 3月5日（日） (13:00-15:00及び15:10-17:10)
時間 講演者・題目 13:00-13:40 宮島信也（早大），荻田武史（JST／早大）, 大石進一（早大）
13:40-14:20 尾崎克久（早大D2），荻田武史（JST／早大），Siegfried M. Rump（TUHH），大石進一（早大）
15:00-15:10 （休憩） 15:10-16:00 Siegfried M. Rump（TUHH）
Accurate Sum and Dot Product
16:00-16:10 （休憩） 16:10-17:00 大石進一（早大）
Convergence of Rump's Method for Inverting Arbitrarily Ill-conditioned Matrices
計算の品質研究部会OSプログラム： 9月23日（金） (9:20-12:00)
時間 講演者・題目 9:20- 9:45 宮島信也（早大・理工），荻田武史（JST／早大・理工）, 大石進一（早大・理工）
10:35-10:45 （休憩） 10:45-11:10 川中子正（東工大・理工学）
日時 10月22日(月) 2:40-4:10
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。
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) 17:10-17:30 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
Workshop on Numerical Calculation with Guaranteed Accuracy
5月8日(火) (午前の部) 10:40-12:10
(特別講演) Ulrich W. Kulisch (Universitaet Karlsruhe, D-76128 Karlsruhe, Germany)
Do we Need and can we Build Better Computers?
(abstract) Advances in computer technology are now so profound that the capability and repertoire of computers can and should be extended. At a time where millions of transistors can be placed on a single chip, where computing speed is measured in GIGAFLOPS and memory space in GIGA-words there is no need anymore to perform all computer operations by the four elementary floating-point operations with all the shortcomings of this methodology. The talk will define advanced computer arithmetic. It extends the accuracy requirement of the elementary floating-point operations - for instance, as defined by the IEEE arithmetic standard -- to all operations in the usual product spaces of computation: the real and complex vector spaces and their interval counterparts. This enhances the mathematical power of the digital computer considerably. The new expanded computational capability is gained at modest cost and even implicates a performance advantage. It is obtained by putting a methodology into modern computer hardware which was already available on old calculators before the electronic computer entered the scene. The new arithmetic increases both, the speed of a computation as well as the accuracy of the computed result. By operator overloading in a programming language a long real arithmetic (array of reals), matrix and vector arithmetic, interval arithmetic, a long interval arithmetic as well as automatic differentiation arithmetic become part of the runtime system of the compiler. This simplifies programming a great deal. For instance, derivatives, Taylor-coefficients, gradients, Jacobian and Hessian matrices or enclosures of these are directly computed out of the expression by a simple type change of the operands. Techniques are now available so that with this expanded capability, the computer itself can be used to appraise the quality and the reliability of the computed results over a wide range of applications. Problem solving routines with automatic result verification have been developed for many standard problems of numerical analysis as for linear or nonlinear systems of equations, for differential or integral equations, etc. as well as for a large number of applications in the engineering and natural sciences. The talk will discuss a variety of basic solutions and applications.
5月8日 (午後の部 オーガナイズドセッション) 14:00--17:00
(1) *Takeshi Ogita (Waseda University), Shin'ichi Oishi (Waseda University) and Yasunori Ushiro (Hitachi Co.) Fast Inclusion and Residual Iteration of Solution of Linear Systems
(2) Daisuke Oishi (University of Tokyo) *Sunao Murashige (University of Tokyo) Shin'ichi Oishi (Waseda University) Numerical verification of solutions of the Chandrasekhar integral equation
(3) Masato KAMIYAMA (University of Tokyo) *Ken HAYAMI (National Institute of Informatics) Sunao MURASHIGE (University of Tokyo) Shin'ichi OISHI (Waseda University) Validated Numerical Solution of Large Scale Eigenvalue Problems
5月9日(水) (午前の部) 10:40-12:10
(特別講演) Ulrich W. Kulisch (Universitaet Karlsruhe, D-76128 Karlsruhe, Germany)
Advanced Arithmetic for the Digital Computer - Design of Arithmetic
(abstract) The speed of digital computers is ever increasing. While emphasis in computing was traditionally on speed, more emphasis can and must now be put on accuracy and reliability of results. Numerical mathematics has devised algorithms that deliver highly accurate and automatically verified results. This means that these computations carry their own accuracy control. However, the arithmetic available on existing processors makes these methods extremely slow. Their implementation requires suitable arithmetic support and powerful programming tools which are not generally available. The talk will define advanced computer arithmetic. It extends the accuracy requirement of the elementary floating-point operations - for instance, as defined by the IEEE arithmetic standard -- to all operations in the usual product spaces of computation: the real and complex vector spaces and their interval correspondents. The talk will discuss the design of arithmetic units for advanced computer arithmetic. The new expanded computational capability is gained at modest cost. It increases both, the speed of a computation as well as the accuracy of the computed result. A new computer operation, the scalar product, is fundamental to the development of advanced computer arithmetic. It will be shown that fixed-point accumulation of products is the fastest way to execute scalar products on the computer. This is the case for all kinds of computers (Personal Computer, Workstation, Mainframe or Super Computer). In contrast to floating-point accumulation, fixed-point accumulation is error free. Not a single bit is lost. With a fast and accurate scalar product, fast multiple precision arithmetic can easily be provided on the computer. Finally it will be shown that on superscalar processors interval operations can be made as fast as simple floating-point operations with only very modest hardware costs. A coprocessor for advanced computer arithmetic has been designed and built in CMOS VLSI-technology at the speakers institute. It speeds up vector, matrix and other operations and computes them to full accuracy or with only one final rounding. It is the first hardware implementation of the "GAMM/IMACS Proposal for Accurate Floating-point Vector Arithmetic."
Literature: Kulisch, U. W.: Advanced Arithmetic for the Digital Computer - Design of Arithmetic Units.: http//www.elsevier.nl/locate/entcs/volume24.html 72 pages.
Kulisch, U. W.: Advanced Arithmetic for the Digital Computer - Interval Arithmetic revisited.: ftp://ftp.iam.uni-karlsruhe.de/pub/documents/kulisch/advarith.ps.gz 63 pages.
5月9日 (午後の部 オーガナイズドセッション) 14:00--17:00
(1) (特別講演) Tetsuro Yamamoto (Ehime University) Sharp error estimates for finite difference method with non-equidistant nodes applied to two-point boundary value problems
(2) Nobito Yamamoto (The University of Electro-Communications) Error estimates of finite element solutions by Spectrum Method with Verified Computation
(3) Masahide Kashiwagi and *Takatomi Miyata (Waseda University) On the Range of Evaluation of Polynomials Using Affine Arithmetic
10月 山本哲朗先生のシンポジウムを共催 その前後にワークショップ開催予定
International Conference on "Recent Advances in Computational Mathematics"
-- organized by Ehime university, -- co-organaized by Japan SIAM, Kochi university, Shimane university, Yamaguchi university
2001 年 10 月 10 -- 13 日 at Hotel JAL CITY Matsuyama, Matsuyama, JAPAN.