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

Applied Numerical Mathematics

Volumn 60, Issue 9, 2010, Pages 924-933

  Parodi, Mauro ^a   Gaggero, Mauro ^a   Storace, Marco ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

Electronic circuit implementation; Multiresolution approximation; Piecewise linear approximation

Indexed keywords

CIRCUIT IMPLEMENTATION; COMPRESSION ALGORITHMS; CONTINUOUS FUNCTIONS; ELECTRONIC CIRCUITS; MODEL REDUCTION STRATEGIES; MULTI-RESOLUTION APPROACH; MULTI-RESOLUTIONS; MULTIRESOLUTION APPROXIMATION; MULTIVARIATE FUNCTION; NESTED FUNCTIONS; PIECEWISE LINEAR APPROXIMATIONS; PIECEWISE-LINEAR; VECTOR FIELDS;

DYNAMICAL SYSTEMS; NONLINEAR DYNAMICAL SYSTEMS; PIECEWISE LINEAR TECHNIQUES;

APPROXIMATION ALGORITHMS;

EID: 77955663241     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2010.05.002     Document Type: Article

References (34)

1. Special issue on sensor networks and applications IEEE Proceedings 91 8 2003
2. W.B. Arthur Complexity and the economy Science 284 5411 1999 107 109
3. J. Ayers, and J. Witting Biomimetic approaches to the control of underwater walking machines Phil. Trans. R. Soc. A 365 2007 273 295
4. B. Carreras, V. Lynch, I. Dobson, and D. Newman Critical points and transitions in an electric power transmission model for cascading failure blackouts Chaos 12 4 2002 985 994
5. E. Chicca, A. Whatley, P. Lichtsteiner, V. Dante, T. Delbruck, P.D. Giudice, R. Douglas, and G. Indiveri Multi-chip pulse-based neuromorphic systems: a communication infrastructure and an application example IEEE Transactions on Circuits and Systems I 54 5 2007 981 993
6. M. Chien, and E. Kuh Solving nonlinear resistive networks using piecewise-linear analysis and simplicial subdivision IEEE Transactions on Circuits and Systems 24 1977 305 317
7. P. Cignoni, L. De Floriani, C. Montani, E. Puppo, R. Scopigno, Multiresolution modeling and visualization of volume data based on simplicial complexes, in: Proceedings of the 1994 Symposium on Volume Visualization (VVS'94), Tysons Corner, Virginia, USA, 1994, pp. 19-26
8. R. Courant Variational methods for the solution of problems of equilibrium and vibration Bull. Am. Math. Soc. 49 1943 1 23
9. P. Echevarria, M. Martínez, J. Echanobe, I. del Campo, and J. Tarela Digital hardware implementation of high dimensional fuzzy systems Applications of Fuzzy Sets Theory Lecture Notes in Computer Science 2007 Springer Berlin 245 252
10. J. Eckmann, and E. Moses Curvature of co-links uncovers hidden thematic layers in the world-wide web P. Natl. Acad. Sci. USA 99 9 2002 5825 5829
11. R. Ferrer i Cancho, and R. Solé The small world of human language P. Roy. Soc. Lond. B Bio. 268 1482 2001 2261 2265
12. M.S. Floater, E. Quak, and M. Reimers Filter bank algorithms for piecewise linear prewavelets on arbitrary triangulations Journal of Computational and Applied Mathematics 119 2000 185 207
13. M.S. Floater, and K. Hormann Surface parameterization: a tutorial and survey N.A. Dodgson, M.S. Floater, M.A. Sabin, Advances in Multiresolution for Geometric Modelling 2005 Springer Berlin 157 186
14. A. Hodgkin, and A. Huxley A quantitative description of membrane current and its application to conduction and excitation in nerve J. Physiol.-London 117 4 1952 500 544
15. E. Izhikevich Which model to use for cortical spiking neurons? IEEE Transactions on Neural Networks 15 5 2004 1063 1070
16. P. Julián, A. Desages, and O. Agamennoni High-level canonical piecewise linear representation using a simplicial partition IEEE Transactions on Circuits and Systems I 46 1999 463 480
17. P. Julián, A. Desages, and B. D'Amico Orthonormal high level canonical PWL functions with applications to model reduction IEEE Transactions on Circuits and Systems I 47 2000 702 712
18. H. Kuhn Some combinatorial lemmas in topology IBM J. of Research and Development 4 1960 518 524
19. H. Kuhn Simplicial approximation of fixed points Proc. Nat. Acad. Sci. USA 61 1968 1238 1242
20. T. Mestl, C. Lemay, and L. Glass Chaos in high dimensional neural and gene networks Physica D 98 1 1996 33 52
21. J. Montoya, and R. Solé Small world patterns in food webs J. Theor. Biol. 214 3 2002 405 412
22. T. Poggi, F. Comaschi, and M. Storace Digital circuit realization of piecewise affine functions with non-uniform resolution: theory and FPGA implementation IEEE Transactions on Circuits and Systems II: Transaction Briefs 57 2 2010 131 135
23. J. Popovic, H. Hoppe, Progressive simplicial complexes, in: Proceedings of the 24th International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH'97), 1997, pp. 217-224
24. L. Repetto, M. Storace, and M. Parodi A method for the approximate synthesis of cellular nonlinear networks - Part 2: Circuit reduction International Journal of Circuit Theory and Applications 31 3 2003 299 313
25. R. Rovatti, A. Ferrari, and M. Borgatti Automatic implementation of piecewise-linear fuzzy systems addressing memory-performance trade-off A. Kandel, G. Langholz, Fuzzy Hardware: Architectures and Applications 1998 Kluwer Academic Publishers Norwell, MA, USA 159 179
26. M. Storace, P. Julián, and M. Parodi Synthesis of nonlinear multiport resistors: a PWL approach IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49 8 2002 1138 1149
27. M. Storace, L. Repetto, and M. Parodi A method for the approximate synthesis of cellular nonlinear networks - Part 1: Circuit definition International Journal of Circuit Theory and Applications 31 3 2003 277 297
28. M. Storace, and O. De Feo Piecewise-linear approximation of nonlinear dynamical systems IEEE Transactions on Circuits and Systems I: Regular Papers 51 4 2004 830 842
29. M. Storace, and M. Parodi Towards analog implementations of PWL two-dimensional non-linear functions International Journal of Circuit Theory and Applications 33 2 2005 147 160
30. M. Storace, and T. Poggi Digital architectures realizing piecewise-linear multi-variate functions: two FPGA implementations International Journal of Circuit Theory and Applications 37 2010 10.1002/cta.610 in press
31. G. Strang Piecewise polynomials and the finite element method Bull. Am. Math. Soc. 79 1973 1128 1137
32. S. Strogatz Exploring complex networks Nature 410 6825 2001 268 276
33. E. Suter A strategy for the construction of piecewise linear prewavelets over type-1 triangulations in any space dimension Mathematical Methods for Curves and Surfaces: Oslo 2000 2001 Vanderbilt University Nashville, TN
34. J. Wijekoon, P. Dudek, Integrated circuit implementation of a cortical neuron, in: Proceedings of the 2008 IEEE International Symposium on Circuits and Systems (ISCAS'08), Seattle, USA, 2008, pp. 1784-1787