High dimensional problems of integration and approximation. In many applications, notably financial mathematics, problems of
integration and approximation of functions in very high dimensions
are of great interest. By finding modern mathematical solutions to
these problems, we will therefore contribute to Australia's future
success in developing innovative technologies for industrial and
economic applications. By researching at an internationally
competitive level and by cooperating with i ....High dimensional problems of integration and approximation. In many applications, notably financial mathematics, problems of
integration and approximation of functions in very high dimensions
are of great interest. By finding modern mathematical solutions to
these problems, we will therefore contribute to Australia's future
success in developing innovative technologies for industrial and
economic applications. By researching at an internationally
competitive level and by cooperating with international experts, we
will have a share in further strengthening the excellent role of
Australian research institutions within the international scientific
community in mathematics and scientific computing.Read moreRead less
Dynamics of eigenvalue/eigenspace algorithms with applications to signal processing. Many problems in signal and systems lead naturally to an eigenvalue/eigenspace determination and tracking problem; for example (acoustic) echo-cancellation, crosstalk suppression in ADSL modems, direction of arrival determination with an array of sensors, linear system identification etc. Exploiting methods from global analysis and dynamical systems theory we will study the available algorithms for eigenspace de ....Dynamics of eigenvalue/eigenspace algorithms with applications to signal processing. Many problems in signal and systems lead naturally to an eigenvalue/eigenspace determination and tracking problem; for example (acoustic) echo-cancellation, crosstalk suppression in ADSL modems, direction of arrival determination with an array of sensors, linear system identification etc. Exploiting methods from global analysis and dynamical systems theory we will study the available algorithms for eigenspace determination to characterise their computational efficiency, accuracy and effectiveness in various data scenarios. The analysis will lead to improved designs for eigenvalue/eigenspace algorithms, as well as design tools to engineer algorithms to specific situations.Read moreRead less
The Time-Varying Eigenvalue Problem with Application to Signal Processing and Control. Linear models are ubiquitous in representing physical processes. Decomposing a linear model into its fundamental components is known as the eigenvalue problem. In applications as wide ranging as astronomy, aircraft control systems, Internet search engines and communication systems, it is necessary to perform this decomposition of a pertinent time varying linear model on the fly. This project aims to develop si ....The Time-Varying Eigenvalue Problem with Application to Signal Processing and Control. Linear models are ubiquitous in representing physical processes. Decomposing a linear model into its fundamental components is known as the eigenvalue problem. In applications as wide ranging as astronomy, aircraft control systems, Internet search engines and communication systems, it is necessary to perform this decomposition of a pertinent time varying linear model on the fly. This project aims to develop significantly faster and more accurate algorithms for this time varying eigenvalue problem than currently exist. Very modern techniques will be employed to achieve this aim, and the potential benefits to Australian hi-tech industries are great.
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Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limit ....Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limitations and the convergence properties of the proposed
algorithms. The outcomes will be widely applicable in modelling of
large scale and complex data as is encountered in areas of
bioinformatics, physics and experimental studies of complex systems.
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