Piecewise linear approximations of multivariate functions: A multiresolution-based compression algorithm suitable for circuit implementation

Authors:
Mauro Parodi;Mauro Gaggero;Marco Storace
Affiliations:
Biophysical and Electronic Engineering Department, University of Genoa, Via Opera Pia 11a, Genova, Italy;Department of Production Engineering, Thermoenergetics, and Mathematical Models, University of Genoa, P.le Kennedy, Pad. D, Genova, Italy;Biophysical and Electronic Engineering Department, University of Genoa, Via Opera Pia 11a, Genova, Italy
Venue:
Applied Numerical Mathematics
Year:
2010

Citing 11
Cited 0

Multiresolution modeling and visualization of volume data based on simplicial complexes

VVS '94 Proceedings of the 1994 symposium on Volume visualization
Chaos in high-dimensional neural and gene networks

Physica D
Progressive simplicial complexes

Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Automatic implementation of piecewise-linear fuzzy systems addressing memory-performance trade-off

Fuzzy hardware
Filter bank algorithms for piecewise linear prewavelets on arbitrary triangulations

Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
A strategy for the construction of piecewise linear prewavelets over Type-1 triangulations in any space dimension

Mathematical Methods for Curves and Surfaces
Towards analog implementations of PWL two-dimensional non-linear functions: Research Articles

International Journal of Circuit Theory and Applications
Some combinatorial Lemmas in topology

IBM Journal of Research and Development
Digital circuit realization of piecewise-affine functions with nonuniform resolution: theory and FPGA implementation

IEEE Transactions on Circuits and Systems II: Express Briefs
Digital architectures realizing piecewise-linear multivariate functions: Two FPGA implementations

International Journal of Circuit Theory and Applications
Which model to use for cortical spiking neurons?

IEEE Transactions on Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is concerned with a multiresolution approach to the piecewise-linear approximation of multivariate nonlinear continuous functions. The proposed technique has no restrictions on the number of variables the functions depend on, and is based on the use of piecewise-linear ''hat'' functions. The approximation levels are related to nested function spaces. The multiresolution approach allows one to define a simple model reduction strategy that is based on a proper error definition. The interest in the piecewise-linear approximations and in the hat functions is motivated by the simplicity of their circuit implementations. The efficiency of the method is tested via two benchmark examples, one of which concerns the approximation of the vector field of a nonlinear dynamical system.