Slides of Lectures

by Arnold Neumaier


It is God's privilege to conceal things, but the kings' pride is to research them.
(Proverbs 25:2)


A= Analysis, C = Combinatorics, F = Foundations,
L = Linear Algebra, N = Numerical Analysis, O = Optimization,
P = Physics/Chemistry, S = Statistics

In many cases, there are associated publications, see Recent Papers and Preprints

N.
A. Neumaier, Rigorously covering all solutions of infinite-dimensional equations, Lecture, 2014.
video of the lecture at BIRS


O.
A. Neumaier, VXQR: Derivative-free unconstrained optimization based on QR factorizations, Slides, 2010.
pdf file (105K)
figures (1429K)

O.
A. Neumaier, AD-like techniques in global optimization, Slides, 2008
pdf file (2283K)

F.
A. Neumaier, FMathL - Formal Mathematical Language, Slides, 2009
pdf file (98K)
Slides for a lecture at the AUTOMATHEŘ 2009 workshop, giving an overview of our work in the FMathL project for creating a modeling and documentation language for mathematics, suited to the habits of mathematicians


NO.
A. Neumaier, Towards optimization-based error bounds for uncertain PDEs, Slides, 2008
pdf file (347K)
Using tools from functional analysis and global optimization, methods are presented for obtaining, given an approximate solution of a partial differential equation, realistic error bounds for some response functional of the solution.

The method is based on computable bounds for the inverse of linear elliptic operators. Like in the dual weighted residual (DWR) method, our error bounds for response functionals have the quadratic approximation property (so that they are asymptotically optimal), but in contrast to DWR, our bounds are rigorous and also capture the higher order contributions to the error.

Using global optimization techniques, bounds can be found that not only cover the errors in solving the differential equations but also the errors caused by the uncertainty in the parameters. This provides reliable tools for the assessment of uncertainty in the solution of elliptic partial differential equations. Our bounds are independent of the way the approximations are obtained, hence can be used to independently verify the quality of an approximation computed by an arbitrary solver. The bounds not only account for discretization errors but also for other numerical errors introduced through numerical integration and boundary aproximations.

We also discuss how to represent model uncertainty in terms of so-called clouds, which describe the rough shapes of typical samples of various size, without fixing the details of the distribution. Clouds use only information from 1- and 2-dimensional marginal distributions, readily available in practice.


P.
A. Neumaier, Optical models for quantum mechanics, Slides of a lecture given on February 16, 2010 at the Institute for Theoretical Physics, University of Giessen.
pdf file (156K)
This lecture (the second of three) discusses work towards a new, classical view of quantum mechanics. It is based on an analysis of polarized light, of the meaning of quantum ensembles in a field theory, of classical simulations of quantum computing algorithms, and resulting optical models for the simulation of quantum mechanics.
In particular, it is shown that classical second-order stochastic optics is precisely the quantum mechanics of a single photon, with all its phenomenological bells and whistles.
P.
A. Neumaier, Classical and quantum field aspects of light, Slides of a lecture given on January 29, 2009 at the Institute of Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Vienna.
pdf file (374K)
This lecture discusses foundational problems on the nature of light revealed by 1. attempts to define a probability concept for photons, 2. quantum models for photons on demands (and their realization through laser-induced emission by a calcium ion in a cavity), 3. models explaining the photo effect, and 4. Bell-type experiments for single photon nonlocality.
O.
A. Neumaier, Global Optimization and Constraint Satisfaction, Slides, 2006.
pdf file (173K)

O.
A. Neumaier, Constrained global optimization, Slides, 2005.
pdf file (225K)

O.
A. Neumaier, Worst case analysis of mechanical structures by interval methods, Slides, 2005.
pdf file (263K)

OS.
A. Neumaier, Uncertainty modeling for robust verifiable design, Slides, 2004.
pdf file (318K)

O.
A. Neumaier and J.-P. Merlet, Constraint satisfaction and global optimization in robotics, Slides, 2002.
pdf file (449K)
























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my home page (http://www.mat.univie.ac.at/~neum)

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)