Browsing by Subject "Matrices."

Now showing 1 - 5 of 5

Open Access
Comparison of several estimators for the covariance of the coefficient matrix
(1995) Orhan, Mehmet
The standard regression analysis assumes that the variances of the disturbance terms are constant, and the ordinary least squares (OLS) method employs this very crucial assumption to estimate the covariance of the disturbance terms perfectly, but OLS fails to estimate well when the variance of the disturbance terms vary across the observations. A very good method suggested by Eicker and improved by White to estimate the covariance matrix of the disturbance terms in case of heteroskedeisticity was proved to be biased. This paper evaluates the performance of White’s method as well as the OLS method in several different settings of regression. Furthermore, bootstrapping, a new method which very heavily depends on computer simulation is included. Several types of this method are used in several cases of homoskedastic, heteroskedastic, balanced, and unbalanced regressions.
Open Access
Free actions on CW-complexes and varieties of square zero matrices
(2011) Şentürk, Berrin
Gunnar Carlsson stated a conjecture which gives a lower bound on the rank of a differential graded module over a polynomial ring with coefficients in algebraically closed field k when it has a finite dimensional homology over k. Carlsson showed that this conjecture implies the rank conjecture about free actions on product of spheres. In this paper, to understand the Carlsson’s conjecture about differential graded modules, we study the structure of the variety of upper triangular square zero matrices and the techniques which were investigated by Rothbach to determine its irreducible components . We hope these varieties could help prove Carlsson’s conjecture.
Open Access
Minimizing communication through computational redundancy in parallel iterative solvers
(2011) Torun, Fahreddin Şükrü
Sparse matrix vector multiplication (SpMxV) of the form y = Ax is a kernel operation in iterative linear solvers used in scientific applications. In these solvers, the SpMxV operation is performed repeatedly with the same sparse matrix through iterations until convergence. Depending on the matrix and its decomposition, parallel SpMxV operation necessitates communication among processors in the parallel environment. The communication can be reduced by intelligent decomposition. However, we can further decrease the communication through data replication and redundant computation. The communication occurs due to the transfer of x-vector entries in row-parallel SpMxV computation. The input vector x of the next iteration is computed from the output vector of the current iteration through linear vector operations. Hence, a processor may compute a y-vector entry redundantly, which leads to a x-vector entry in the following iteration, instead of receiving that x-vector entry from another processor. Thus, redundant computation of that y-vector entry may lead to reduction in communication. In this thesis, we devise a directed-graph-based model that correctly captures the computation and communication pattern for above-mentioned iterative solvers. Moreover, we formulate the communication minimization by utilizing redundant computation of y-vector entries as a combinatorial problem on this directed graph model. We propose two heuristics to solve this combinatorial problem. Experimental results indicate that the communication reducing strategy by redundantly computing is promising.
Open Access
A social accounting matrix multiplier analysis of the effects of agricultural support policies: the case of US
(1997) Tin, Ela
This study investigates the economywide effects of agricultural support policies in the US, with special reference to changes required by the Uruguay Round Agreement on Agriculture. For this purpose, the relevant multipliers are derived using a Social Accounting Matrix (SAMs) framework that is known to be capable of describing certain structural features of an economy by capturing the interactions between various micro and macro accounts. Following a discussion on their theoretical derivation and decomposition, SAM multipliers are computed at two different levels of aggregation, and are used to investigate the effects of a switch to decoupled support to US farming on the US economy.
Open Access
Stability robustness of linear systems: a field of values approach
(1997) Saadaoui, Karim
One active area of research in stability robustness of linear time invariant systems is concerned with stability of matrix polytopes. Various structured real parametric uncertainties can be modeled by a family of matrices consisting of a convex hull of a finite number of known matrices, the matrix poly tope. An interval matrix family consisting of matrices whose entries can assume any values in given intervals are special types of matrix polytopes and it models a commonly encountered parametric uncertainty. Results that allow the inference of the stability of the whole polytope from stability of a finite number of elements of the polytope are of interest. Deriving such results is known to be difficult and few results of sufficient generality exist. In this thesis, a survey of results pertaining to robust Hurwitz and Schur stability of matrix polytopes and interval matrices are given. A seemingly new tool, the field of values, and its elementary properties are used to recover most results available in the literature and to obtain some new results. Some easily obtained facts through the field of values approach are as follows. Poly topes with normal vertex matrices turn out to be Hurwitz and Schur stable if and only if the vertex matrices are Hurwitz and Schur stable, respectively. If the polytope contains the transpose of each vertex matrix, Hurwitz stability of the symmetric part of the vertices is necessary and sufficient for the Hurwiz stability of the polytope. If the polytope is nonnegative and the symmetric part of each vertex matrix is Schur stable, then the polytope is also stable. For polytopes with spectral vertex matrices, Schur stability of vertices is necessary and sufficient for the Schur stability of the polytope.