| dc.contributor.author | Huang, Wanzhen. | en_US |
| dc.date.accessioned | 2014-10-21T12:36:50Z | |
| dc.date.available | 1993 | |
| dc.date.issued | 1993 | en_US |
| dc.identifier.other | AAINN93678 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/55384 | |
| dc.description | The problem of estimating a (non-negative) density function, given a finite number of its moments, arises in numerous practical applications. By introducing an entropy-like objective function, we are able to treat this problem as an infinite-dimensional convex programming problem. | en_US |
| dc.description | The convergence of our estimate to the underlying density is dependent on the choice of the objective. In this thesis, I studied the most commonly used classes of objectives, which include the Boltzmann-Shannon entropy, the Fermi-Dirac entropy, the truncated $L\sb{p}$-entropy. First, I discussed the duality properties of the convex program ($P\sb{n}$), which involves only n moments, and gave theorems to estimate the bounds of the dual gaps. After proving a general necessary optimality condition and giving rates of norm convergence, I set up a set of uniform convergence theorems for certain choices of entropies, provided that the moment functions are algebraic or trigonometric polynomials. | en_US |
| dc.description | In Chapter 4, I used Newton's method to solve the dual problem. I compared the computational results of the problem with various choices of entropies. For the problem with the Boltzmann-Shannon entropy, using a special structure among the moments, I have developed a set of very efficient algorithm. By using some additional moments, within much less time, we can find a very good estimate function to the underlying density by solving just a couple of linear systems. The algorithms have been implemented in Fortran. Some 2- and 3-dimensional examples have been tested. Since the algorithm is heuristic instead of iterative, some related error analysis has also been performed. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 1993. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | Linearly constrained convex programming of entropy type: Convergence and algorithms. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
