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Now showing items 1-10 of 693

#### Workload Matters: A Robust Approach to Physical RDF Database Design

(University of Waterloo, 2015-10-01)

Recent advances in Information Extraction, Linked Data Management and the Semantic Web have led to a rapid increase in both the volume and the variety of publicly available graph-structured data. As more and more businesses ...

#### On primal-dual interior-point algorithms for convex optimisation

(2015-09-29)

This thesis studies the theory and implementation of interior-point methods
for convex optimisation. A number of important problems from mathematics and
engineering can be cast naturally as convex optimisation ...

#### The Valuation and Risk Management of a DB Underpin Pension Plan

(University of Waterloo, 2007-08-02)

Hybrid pension plans offer employees the best features of both defined benefit and defined contribution plans. In this work, we consider the hybrid design offering a
defined contribution benefit with a defined benefit ...

#### Stochastic Mortality Models with Applications in Financial Risk Management

(University of Waterloo, 2007-06-18)

In product pricing and reserving, actuaries are often required to make predictions of future death rates. In the past, this has been performed by using deterministic improvement scales that give only a single mortality ...

#### Combinatorial Constructions for Transitive Factorizations in the Symmetric Group

(University of Waterloo, 2004)

We consider the problem of counting <i>transitive factorizations</i> of permutations; that is, we study tuples (σ<i>r</i>,. . . ,σ1) of permutations on {1,. . . ,<i>n</i>} such that (1) the product ...

#### Properties of graphs with large girth

(University of Waterloo, 2008-01-24)

This thesis is devoted to the analysis of a class of
iterative probabilistic algorithms in regular graphs, called
locally greedy algorithms, which will provide bounds for
graph functions in regular graphs with ...

#### Numerical Stability in Linear Programming and Semidefinite Programming

(University of Waterloo, 2006)

We study numerical stability for interior-point methods applied to Linear Programming, LP, and Semidefinite Programming, SDP. We analyze the difficulties inherent in current methods and present robust algorithms. <br /><br /> We start with the error bound analysis of the search directions for the normal equation approach for LP. Our error analysis explains the surprising fact that the ill-conditioning is not a significant problem for the normal equation system. We also explain why most of the popular LP solvers have a default stop tolerance of only 10<sup>-8</sup> when the machine precision on a 32-bit computer is approximately 10<sup>-16</sup>. <br /><br /> We then propose a simple alternative approach for the normal equation based interior-point method. This approach has better numerical stability than the normal equation based method. Although, our approach is not competitive in terms of CPU time for the NETLIB problem set, we do obtain higher accuracy. In addition, we obtain significantly smaller CPU times compared to the normal equation based direct solver, when we solve well-conditioned, huge, and sparse problems by using our iterative based linear solver. Additional techniques discussed are: crossover; purification step; and no backtracking. <br /><br /> Finally, we present an algorithm to construct SDP problem instances with prescribed strict complementarity gaps. We then introduce two

**measures of strict complementarity gaps**. We empirically show that: (i) these measures can be evaluated accurately; (ii) the size of the strict complementarity gaps correlate well with the number of iteration for the SDPT3 solver, as well as with the local asymptotic convergence rate; and (iii) large strict complementarity gaps, coupled with the failure of Slater's condition, correlate well with loss of accuracy in the solutions. In addition, the numerical tests show that there is no correlation between the strict complementarity gaps and the geometrical measure used in [31], or with Renegar's condition number....#### Bayesian Inference for Stochastic Volatility Models

(University of Waterloo, 2012-09-26)

Stochastic volatility (SV) models provide a natural framework for a
representation of time series for financial asset returns. As a
result, they have become increasingly popular in the finance
literature, although they ...

#### Multivariate Longitudinal Data Analysis with Mixed Effects Hidden Markov Models

(University of Waterloo, 2013-01-24)

Longitudinal studies, where data on study subjects are collected over time, is increasingly involving multivariate longitudinal responses. Frequently, the heterogeneity observed in a multivariate longitudinal response can ...

#### Free semigroup algebras and the structure of an isometric tuple

(University of Waterloo, 2011-06-28)

An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ...