A methodology for the constructive approximation of nonlinear operators defined on noncompact sets

References

• Barron , A. R. 1993 . Universal approximation bounds for superpositions of a sigmoidal function . IEEE Trans. Info. Th. , 39 ( 3 ) : 930 – 945 .
   Web of Science ®Google Scholar
• Bruno , V. I. 1984 . Approximation Theory . An approximate Weierstrass theorem in topological vector space, J. , 42 ( 3 ) : 1 – 3 .
   Google Scholar
• Cybenko , G. 1989 . Approximation by superpositions of a sigmoidal function . Math. Control Signals Systems , 2 ( 3 ) : 303 – 314 .
   Google Scholar
• Daugavet , I. K. and Lanne , A. A. 1985 . Siberian Mathematical Journal . On polynomial approximation of non-linear operators in the space C , 26 ( 3 ) : 44 – 48 .
   Google Scholar
• Dunford , N. and Schwartz , J. 1958 . Linear operators Part 1 , New York : General theory, Inter-science .
   Google Scholar
• Dunford , N. and Schwartz , J. 1958 . Linear operators Part 2 , New York : Spectral theory, Inter-science .
   Google Scholar
• Fox , L. and Parker , I. B. 1972 . “ Chebyshev Polynomials in Numerical Analysis, Oxford Mathematical Handbooks ” . Oxford University Press .
   Google Scholar
• Gallman , P. G. and Narendra , K. S. 1976 . Automatica . Representations of non-linear systems via the Stone-Weierstrass theorem , 12 : 619 – 622 .
   Google Scholar
• Howlett , P. G. and Torokhti , A. P. Modelling of non-linear systems on empirical data . Proceedings of the Conference on Circuits, Systems and Computers ‘96 . Vol. 96 , Greece : Hellenic Naval Academy . to appear
   Google Scholar
• Howlett , P. G. and Torokhti , A. P. Non-linear operator approximation in the synthesis of signal processing systems . Proc. of the Fourth IMA Conference on Mathematics in Signal Processing . U.K. : University of Warwick . to appear
   Google Scholar
• Istrǎţtescu , V. I. 1977 . J. Approximation Theory . A Weierstrass theorem for real Banach spaces , 19 : 118 – 122 .
   Google Scholar
• Kelley , J. 1957 . “ General Topology ” . Princeton, N. J : Van Nostrand .
   Google Scholar
• Porter , W. An overview of polynomic system theory . Proc. IEEE . pp. 36 – 44 .
   Google Scholar
• Prenter , P. M. 1970 . J. Approximation Theory . A Weierstrass theorem for real, separable Hilbert spaces , 3 : 341 – 357 .
   Google Scholar
• Prolla , J. B. and Machado , S. 1982 . J. Approx. Theory . Weierstrass-Stone theorems for set-valued mappings , 36 : 1 – 15 .
   Google Scholar
• Gould , B. 1975 . “ Theory and application of digital processing signals ” . Englewood Cliffs, N. J. : Prentice-Hall .
   Google Scholar
• Rudin , W. 1976 . “ Principles of Mathematical Analysis ” . New York : McGraw-Hill .
   Google Scholar
• Sazonov , B. 1958 . A remark about characteristic functionals . Probability Theory and its Applications , 3 : 201 – 205 .
   Google Scholar
• Schaefer , H. S. 1971 . “ Topological vector spaces ” . Springer Verlag Third Printing
   Google Scholar
• Slepian , D. 1978 . The Bell System Technical Journal . Prolate spheroidal wave Junctions, Fourier analysis and uncertainty V:the discrete case , 5 : 1371 – 1430 .
   Google Scholar
• Torokhti , A. P. 1989 . “ Electronic Modelling ” . In On polynomial synthesis of non-linear systems , Vol. 11 , 28 – 34 . Journal of the USSR Academy of Sciences . in Russian
   Google Scholar
• Torokhti , A. P. 1990 . “ Electronic Modelling ” . In Modelling of non-linear dynamical systems , Vol. 6 , 10 – 16 . Journal of the USSR Academy of Sciences . in Russian
   Google Scholar
• Torokhti , A. P. 1990 . Izv. VUZ. Mathematics . On constructive restoration of continuous maps of Banach Spaces , 1 : 86 – 89 . in Russian
   Google Scholar
• Torokhti , A. P. 1991 . Izv. VUZ. Mathematics . On constructive approximation of non-linear operators , 7 : 24 – 28 . in Russian
   Google Scholar
• Torokhti , A. P. and Howlett , P. G. “ J. Aust. Math. Soc ” . In On the constructive approximation of non-linear operators in the modelling of dynamical systems , B to appear
   Google Scholar
• Torokhti , A. , Gray , D. , Elhay , S. , Moran , W. and Howlett , P. A new technique for multidimensional Signal Compression . Proc. of the Fourth International Symposium on Signal Processing and its Applications ISSPA96 . Vol. 1 , pp. 162 – 165 .
   Google Scholar
• Elhay , S. , Moran , W. , Howlett , P. and Gray , D. Discrete rational tree transforms . Proc. of the Fourth International Symposium on Signal Processing and its Applications ISSPA96 . Vol. 1 , pp. 425 – 426 .
   Google Scholar
• Torokhti , A. , Elhay , S. , Moran , W. , Howlett , P. and Gray , D. Hierarchical methods in matrix approximation . Proc. of the Fourth IMA Conference on Mathematics in Signal Processing . U.K. : University of Warwick . to appear
   Google Scholar