https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:46430 Wed 23 Nov 2022 10:54:19 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28123 Wed 11 Apr 2018 16:48:23 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13008 Wed 11 Apr 2018 16:41:49 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13010 p norms, such properties are termed "strong rotundity." A very simple characterization of strongly rotund integral functionals on L₁ is presented that shows, for example, that the Boltzmann-Shannon entropy ∫ x log x is strongly rotund. Examples are discussed, and the existence of everywhere- and densely-defined strongly rotund functions is investigated.]]> Wed 11 Apr 2018 16:19:45 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12986 n^(−a)(−z)~C(a,z)n^−a/2−1/4e2^√nz. We introduce a computationally motivated contour integral that allows efficient numerical Laguerre evaluations yet also leads to the complete asymptotic series over the full parameter domain of subexponential behavior. We present a fast algorithm for symbolic generation of the rather formidable expansion coefficients. Along the way we address the difficult problem of establishing effective (i.e., rigorous and explicit) error bounds on the general expansion. A primary tool for these developments is an “exp-arc” method giving a natural bridge between converging series and effective asymptotics.]]> Wed 11 Apr 2018 15:46:16 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12982 Wed 11 Apr 2018 15:25:51 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13025 Wed 11 Apr 2018 15:14:12 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13022 Wed 11 Apr 2018 14:18:53 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13019 Wed 11 Apr 2018 14:14:13 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13031 p space, subject to a finite number of linear equality constraints. Such problems arise in spectralestimation, where the objective function is often entropy-like, and in constrained approximation. The Lagrangian dual problem is finite-dimensional and unconstrained. Under a quasi-interior constraint qualification, the primal and dual values are equal, with dual attainment. Examples show the primal value may not be attained. Conditions are given that ensure that the primal optimal solution can be calculated directly from a dual optimum. These conditions are satisfied in many examples.]]> Wed 11 Apr 2018 14:04:12 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:20458 Wed 11 Apr 2018 13:51:05 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13038 m given some of its algebraic or trigonometric moments. Using the special structure of this kind of problem, a useful linear relationship among the moments is derived. A simple algorithm then provides a fairly good estimate of x̅ by just solving a couple of linear systems. Numerical computations make the algorithm seem reasonable although the theoretical convergence is still an open problem. Some notes about the error bounds are given at the end of the paper.]]> Wed 11 Apr 2018 13:50:46 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13018 Wed 11 Apr 2018 13:41:04 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13086 Wed 11 Apr 2018 13:17:03 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13006 1-if Y_n converges weakly to ̅y and I(y_n) converges to I( ̅y ), then y_nn converges to ̅y in norm. As a corollary, it is obtained that, as the number of given moments increases, the best entropy estimates converge in L₁ norm to the best entropy estimate of the limiting problem, which is simply ̅ x in the determined case. Furthermore, for classical moment problems on intervals with ̅ x strictly positive and sufficiently smooth, error bounds and uniform convergence are actually obtained.]]> Wed 11 Apr 2018 12:55:45 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13023 m → R is arcwise essentially smooth on R^m and each function f_j : R^n → R, 1 ≤ j ≤ m, is strictly differentiable almost everywhere in Rⁿ, then g ○ f is strictly differentiable almost everywhere in Rⁿ, where f ≡ (f₁,f₂,...,f_m). We also show that all the semismooth and all the pseudoregular functions are arcwise essentially smooth. Thus, we provide a large and robust lattice algebra of Lipschitz functions whose generalized derivatives are well behaved.]]> Wed 11 Apr 2018 12:51:09 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:7551 Wed 11 Apr 2018 12:35:57 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12987 Wed 11 Apr 2018 12:35:27 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13024 Wed 11 Apr 2018 11:35:23 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12787 Wed 11 Apr 2018 11:18:59 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12981 Wed 11 Apr 2018 09:49:51 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13033 Wed 11 Apr 2018 09:38:45 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13093 Wed 11 Apr 2018 09:31:47 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12786 Wed 11 Apr 2018 09:26:19 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13096 p spectral estimation problem. The authors use a new constraint qualification (BWCQ) for infinite-dimensional convex programs with linear type constraints recently introduced in [Borwein and Wolkowicz, Math. Programming, 35 (1986), pp. 83-96]. This allows direct derivation of the explicit optimal solution of the problem as presented in [Goodrich and Steinhardt, SIAM J. Appl. Math., 46 (1986), pp. 417-426], and establishment of the existence of a simple and computationally tractable unconstrained Lagrangian dual problem. Moreover, the results illustrate that (BWCQ) is more appropriate to spectral estimation problems than the traditional Slater condition (which may only be applied after transformation of the problem into an L_p space [Goodrich and Steinhardt, op. cit.] and which therefore yields only necessary conditions).]]> Tue 28 May 2019 16:25:49 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:35894 Tue 14 Jan 2020 10:59:47 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:36669 Mon 04 Sep 2023 11:41:15 AEST ]]>