APPROXIMATION OF BOUNDS ON MIXED-LEVEL ORTHOGONAL ARRAYS

Download

index.pdf

Date

2011-06-01

Author

Sezer, Ali Devin
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

209
views

0
downloads

Mixed-level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao- and Gilbert-Varshamov-type bounds for mixed-level orthogonal arrays. The computational complexity of the terms involved in the original combinatorial representations of these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms. The first is a recursive algorithm that computes the bounds exactly, the second is based on an asymptotic analysis, and the third is a simulation algorithm. They are all based on the representation of the combinatorial expressions that appear in the bounds as expectations involving a symmetric random walk. The Markov property of the underlying random walk gives the recursive formula to compute the expectations. A large deviation (LD) analysis of the expectations provides the asymptotic algorithm. The asymptotically optimal importance sampling (IS) of the same expectation provides the simulation algorithm. Both the LD analysis and the construction of the IS algorithm use a representation of these problems as a sequence of stochastic optimal control problems converging to a limit calculus of a variations problem. The construction of the IS algorithm uses a recently discovered method of using subsolutions to the Hamilton-Jacobi-Bellman equations associated with the limit problem.

Subject Keywords

Mixed-level orthogonal array, Rao bound, Gilbert–Varshamov bound, Error block code, Counting, İmportance sampling, Large deviation, Optimal control, Asymptotic analysis, Subsolution approach, Hamilton–Jacobi–Bellman equation

URI

https://hdl.handle.net/11511/32389

Journal

ADVANCES IN APPLIED PROBABILITY

DOI

https://doi.org/10.1017/s0001867800004912

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Development of an incompressible navier-stokes solver with alternating cell direction implicit method on structured and unstructured quadrilateral grids Baş, Onur; Tuncer, İsmail Hakkı; Department of Aerospace Engineering (2007) In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping m...
Multi objective conceptual design optimization of an agricultural aerial robot (AAR) Özdemir, Segah; Tekinalp, Ozan; Department of Aerospace Engineering (2005) Multiple Cooling Multi Objective Simulated Annealing algorithm has been combined with a conceptual design code written by the author to carry out a multi objective design optimization of an Agricultural Aerial Robot. Both the single and the multi objective optimization problems are solved. The performance figures of merits for different aircraft configurations are compared. In this thesis the potential of optimization as a powerful design tool to the aerospace problems is demonstrated.
Parallel solution of soil-structure interaction problems on pc clusters Bahçecioğlu, Tunç; Çetin, Kemal Önder; Department of Civil Engineering (2011) Numerical assessment of soil structure interaction problems require heavy computational efforts because of the dynamic and iterative (nonlinear) nature of the problems. Furthermore, modeling soil-structure interaction may require ﬁner meshes in order to get reliable results. Latest computing technologies must be utilized to achieve results in reasonable run times. This study focuses on development and implantation of a parallel dynamic ﬁnite element analysis method for numerical solution of soil-structure i...
Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients Elfarra, Monier Ali; Akmandor, İbrahim Sinan; Department of Aerospace Engineering (2005) In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key ...
Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem Koc, S; Song, JM; Chew, WC (Society for Industrial & Applied Mathematics (SIAM), 1999-04-29) The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate-but fast-methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtain...

Citation Formats

A. D. Sezer and F. Özbudak, “APPROXIMATION OF BOUNDS ON MIXED-LEVEL ORTHOGONAL ARRAYS,” ADVANCES IN APPLIED PROBABILITY, pp. 399–421, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32389.