Publication Cover
Applicable Analysis
An International Journal
Volume 58, 1995 - Issue 3-4
20
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Fast heuristic methods for function reconstruction using derivative information

, &
Pages 241-261 | Received 25 Nov 1994, Published online: 02 May 2007

  • Borwein , J.M. and Huang , W.Z. A heuristic method for polynomial moment problems with Boltzmann-Shannon entropy . SIAM J. Optimization, in press. ,
  • Borwein , J.M. and Lewis , A.S. 1991 . Convergence of best entropy estimates . SIAM J. Optimization , 1 : 191 – 205 .
  • Borwein , J.M. and Lewis , A.S. 1991 . On the convergence of moment problems . Transactions of the Amer. Math. Soc. , 325 : 245 – 271 .
  • Borwein , J.M. and Lewis , A.S. 1993 . Partially-finite programming in L1: entropy maximization . SIAM J. Optimization , 3 : 248 – 267 .
  • Browein , J.M. and Lewis , A.S. 1991 . Duality relationships for entropy-like minimization problems . SIAM J. Control Optimiz. , 29 : 325 – 338 .
  • Borwein J.M. Lewis A.S. Noll D. Maximum entropy reconstruction using derivative information, part I: Fisher information and convex duality, Mathematics of Operations Research, to appear.
  • Borwein , J.M. , Lewis , A.S. , Limber , M.N. and Noll , D. Maximum entropy reconstruction using derivative information, part II: Computational Results . J. of Numerical Mathematics, to appear. ,
  • Brockwell , P.J. and Davis , R.A. 1991 . Time Series: Theory and Methods , Springer Verlag .
  • Buck , B. and MacAuley , V.A. 1991 . Maximum Entropy in Action , Oxford : Oxford Science Publ. .
  • Burg , J.P. 1967 . “ Maximum entropy spectral analysis, 37th meeting of the Society of Exploration Geophysicists ” . Oklahoma City
  • Csiszar , I. 1967 . Information-type measures of difference of probability distributions and indirect observations . Studia Sci. Math. Hungar. , 2 : 299 – 318 .
  • Dacunha-Castelle , D. and Gamboa , F. 1990 . Maximum d'entropie et problème des moments . Ann. Inst. Henri Poincaré , 26 : 567 – 596 .
  • Decarreau , A. , Hilhorst , D. , Lemaréchal , C. and Navaza , J. 1992 . Dual methods in entropy maximization: Application to some problems in crystallography . SIAM J. Optimization , 2 : 173 – 197 .
  • Fletcher , R. 1987 . “ Practical Methods of Optimization ” . New York : John Wiley & Sons .
  • Gamboa , F. 1989 . “ Méthode du maximum d'entropie sur la moyenne et applications, Thése ” . Univ. Paris Sud .
  • Goodrich , R.K. and Steinhardt , A. 1986 . L2 spectral estimation . SIAM J. Applied Math. , 46 : 417 – 428 .
  • Jaynes , E.T. 1968 . Prior probabilities . IEEE Transactions , SSC-4 : 227 – 241 .
  • Jaynes , E.T. 1982 . On the rationale of maximum entropy metyhods . Proc. IEEE, Special issue on spectral estimation , 70 : 939 – 952 .
  • Johnson , R.W. and Shore , J.E. 1984 . Which is the better entropy expression for speech processing: -SlogS or log S? . IEEE Transactions on Acoustics, Speech and Signal Processing , ASSP-32 : 129 – 137 .
  • Karlin , S. and Studden , W.J. 1966 . Tchebysheff Systems: With applications in Analysis and Statistics , New York : Wiley .
  • Kelly , J.E. 1960 . The cutting-plane method for solving convex problems . J. Soc. Indust. Appl. Math. , 8 ( 4 ) : 703 – 712 .
  • Liese , F. and Vajda , I. 1987 . “ Convex statistical distances ” . Leipzig : Teubner .
  • McClellan , J.H. and Lang , S.W. 1982 . “ Multi-dimensional MEM spectral estimation, Spectral Analysis and its use in underwater acoustics ” . 10.1 – 10.8 . London, U.K. : Imperial College . Institute of Acoustics.
  • Noll , D. Rates of convergence for best entropy estimates . Statistics and Decisions, to appear. ,
  • Rockafellar , R.T. 1970 . “ Convex Analysis ” . Princeton Univ. Press .
  • Schmidt , J.W. 1991 . Dual algorithms for solving convex partially finite optimization problems . DMV Mitteilungen ,
  • Silver , R.N. 1992 . Quantum statistical inference . IEEE Proc. ,
  • Skilling , J. , ed. 1989 . Maximum-entropy and Bayesian methods , Dordrecht, The Netherlands : Kluwer .
  • Teboulle , M. and Vajda , I. 1992 . Convergence of best ⊘-entropy estimates . IEEE Trans. Inform. Theory ,

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.