Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Maud Lindström litemat@mai.liu.se senast torsdagar kl 12.00.

Vi har dessutom ett arkiv av gamla nummer.

v9 1998

Föreläsningar

Matematiska kollokviet

Fredagen den 20 februari kl. 13.15-14.15 talar Jan-Åke Larsson om

Bells olikhet: kan man beskriva små objekt med sannolikhetslära?

Lokal: MAI:s seminarierum Beurling.

Lars Inge Hedberg

Doktorandkurs

Iterative Methods for Linear Systems The course will cover modern iterative methods for solving linear systems, typically derived from discretization of PDEs.

The course will start with a brief review of classical methods based on matrix splittings. The first main topic will be projection methods, in particular Krylov subspace methods. Preconditoned iterations and different classes of preconditioners will be the second main topic.

A reasonable knowledge of linear algebra, including canonical forms of matrices and matrix computations, will be assumed.

First lecture: Thursday, Feb. 26, 10-12.

Place: MAI:s seminarierum, Beurling.

The main textbook will be:

Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Co., 1996.

Åke Björck and Tommy Elfving

Seminarium i Tillämpad Matematik/Numerisk Analys

Fredagen den 27 februari, 13.15-14.15 talar Prof. Raytcho Lazarov, Texas A&M University om

Least-squares Finite Element Approximations to Second Order Elliptic Problems

(Joint work with J. Bramble and J. Pasciak)

Abstract:

We consider general second order elliptic equation written as a system of first order. This formulation is natural and introduces the flux (the scaled gradient) as a new dependent variable. The weak formulation of this system leads to a saddle point problem which is subject to the inf-sup condition. The inf-sup condition poses restrictions on finite element spaces when finite element method is employed and leads to indefinite algebraic systems.

We introduce three possible least-squares functionals for the system of first order. Subject to some regularity conditions their minimization recovers the solution. All formulations lead to finite element systems with symmetric and positive definite matrices. We discuss briefly the merits and the deficiencies of the three least squares formulations. The main objective of the talk is to describe and to analyze the formulation based on a discrete minus one inner product.

Lokal: MAI:s seminarierum Beurling, ing. B23-25, 1 tr

Lars Inge Hedberg och Åke Björck

Seminarium i optimeringslära

Fredagen den 20 februari, kl 10.15 talar Karen Aardal, Department of Computer Science, Utrecht University, om

An algorithm for solving a system of diophantine equations with lower and upper bounds on the variables

Abstract: We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction, and first finds short vectors satisfying the diophantine equations. The next step is to branch on linear combinations of these vectors, which either yields a vector that satisfies the bound constraints or provides a proof that no such vector exists. The research was motivated by the need for solving constrained diophantine equations as subproblems when designing integrated circuits for video signal processing. Our algorithm is tested with good result on real-life data. This is joint work with Arjen Lenstra and Cor Hurkens.

Lokal: MAI:s seminarierum Beurling.

Alla intresserade är välkomna!
Maud Göthe Lundgren

Anspråkslösa seminariet

Tisdagen den 24 februari kl. 10.15 talar Krzysztof Marciniak om Liouvilles integrabilitetssats.

Lokal: Beurling.

Hans Lundmark och Claes Waksjö

Informellt seminarium
Optimeringslära

Onsdagen den 25 februari kl 15.15 talar
Patrik Flisberg om

Minimization of maximal torque of a flywheel robot concept

Abstract:

This talk treats the optimization of the Linköping Flywheel Robot with respect to maximal torque. The robot has three links, and the robot manipulator could shortly be described as a rotating arm with constant angle velocity for major displacement and two tiny links for local X-Y positioning.

Minimizing the maximal torque of the joints will keep the size of the robot parts down, the wear and tear and hence the cost.

Given the vector
of relative angles of the different joints, as functions of time, as well as its derivatives and , the torques can be computed through a triangular system, given by the Newton-Euler equations.

Due to the complex dependence of the torques of the angle vector , it is a complicated control problem to minimize the maximal torque. We approximate the angle function by B-splines.

The solution technique will be presented and computational results for typical cases. In particular, we have been able to achieve a 30 % reduction of the maximum torque, as compared to earlier results obtained with simpler techniques. Some extensions of the problem will also be discussed.

Lokal: Kompakta rummet

Välkomna!

Presentation av examensarbete

Fredagen den 27 februari kl 13.15-15.00 presenterar Kennet Melin sitt examensarbete med titeln Planering av tomvagnstransporter hos SJ: En Lagrangeheuristik för flervaruflödesproblemet med fasta kostnader på väg.

Lokal: Determinanten.

Välkomna!
Kaj Holmberg

Mer information om MAI finns på under MAIs hemsida
Material till Lite Mat lämnas till Maud Lindström senast torsdagar kl 12.00.
Tel 013-281405, Fax 013-100746, Email: litemat@mai.liu.se
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