Slides of Lectures
by Arnold Neumaier
It is God's privilege to conceal things,
but the kings' pride is to research them.
A= Analysis, C = Combinatorics, F = Foundations,
L = Linear Algebra, N = Numerical Analysis, O = Optimization,
P = Physics/Chemistry, S = Statistics
In some cases, there are associated publications, see
Recent Papers and Preprints
Artificial Intelligence, Mathematics, and Consciousness,
Rigorously covering all solutions of infinite-dimensional equations,
video of the lecture at BIRS
VXQR: Derivative-free unconstrained optimization based on QR
pdf file (105K)
AD-like techniques in global optimization,
pdf file (2283K)
FMathL - Formal Mathematical Language,
pdf file (98K)
Slides for a lecture at the
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
Towards optimization-based error bounds for uncertain PDEs,
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
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.
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.
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
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.
Global Optimization and Constraint Satisfaction,
pdf file (173K)
Constrained global optimization,
pdf file (225K)
Worst case analysis of mechanical structures by interval methods,
pdf file (263K)
Uncertainty modeling for robust verifiable design,
pdf file (318K)
A. Neumaier and J.-P. Merlet,
Constraint satisfaction and global optimization in robotics,
pdf file (449K)
Computational Mathematics Links
home page (http://www.mat.univie.ac.at/~neum)
Arnold Neumaier (Arnold.Neumaier@univie.ac.at)