Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. "The Newton Summer Academy is a program intervention funded by the National Science Foundation. It was developed at the University of Missouri-Columbia by a team of scientists, instruction and curriculum personnel, and educators."--Leaf 8. "The present study sought to investigate the saliency of social cognitive factors in the career decision-making processes of bright, adolescent females. In addition, the present study aimed to gain empirical information about the effectiveness of the Newton Summer Academy, a National Science Foundation intervention program."--Leaf [12]. Includes bibliographical references (leaves 141-162). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. "The Newton Summer Academy is a program intervention funded by the National Science Foundation. It was developed at the University of Missouri-Columbia by a team of scientists, instruction and curriculum personnel, and educators."--Leaf 8. "The present study sought to investigate the saliency of social cognitive factors in the career decision-making processes of bright, adolescent females. In addition, the present study aimed to gain empirical information about the effectiveness of the Newton Summer Academy, a National Science Foundation intervention program."--Leaf [12]. Includes bibliographical references (leaves 141-162). Also available on the Internet.

Thesis (Ph. D.)--York University, 2001. Graduate Programme in Mathematics. / Typescript. Includes bibliographical references (leaves 114-119). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66358.

The numerical solution of Stein (aka discrete Lyapunov) equations is the primary step in Newton's method for the solution of discrete-time algebraic Riccati equations (DARE). Here we present a low-rank Smith method as well as a low-rank alternating-direction-implicit-iteration to compute low-rank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.

Une arithmétique sûre et efficace est un élément clé pour exécuter des calculs rapides et sûrs. Le choix du système numérique et des algorithmes arithmétiques est important. Nous présentons une nouvelle représentation des nombres, les "RN-codes", telle que tronquer un RN-code à une précision donnée est équivalent à l'arrondir au plus près. Nous donnons des algorithmes arithmétiques pour manipuler ces RN-codes et introduisons le concept de "RN-code en virgule flottante." Lors de l'implantation d'une fonction f en arithmétique flottante, si l'on veut toujours donner le nombre flottant le plus proche de f(x), il faut déterminer si f(x) est au-dessus ou en-dessous du plus proche "midpoint", un "midpoint" étant le milieu de deux nombres flottants consécutifs. Pour ce faire, le calcul est d'abord fait avec une certaine précision, et si cela ne suffit pas, le calcul est recommencé avec une précision de plus en plus grande. Ce processus ne s'arrête pas si f(x) est un midpoint. Étant donné une fonction algébrique f, soit nous montrons qu'il n'y a pas de nombres flottants x tel que f(x) est un midpoint, soit nous les caractérisons ou les énumérons. Depuis le PowerPC d'IBM, la division en binaire a été fréquemment implantée à l'aide de variantes de l'itération de Newton-Raphson dues à Peter Markstein. Cette itération est très rapide, mais il faut y apporter beaucoup de soin si l'on veut obtenir le nombre flottant le plus proche du quotient exact. Nous étudions comment fusionner efficacement les itérations de Markstein avec les itérations de Goldschmidt, plus rapides mais moins précises. Nous examinons également si ces itérations peuvent être utilisées pour l'arithmétique flottante décimale. Nous fournissons des bornes d'erreurs sûres et précises pour ces algorithmes.

Šiame darbe buvo analizuojama Niutono fraktalų Žulija aibės. Dažniausiai Žulija ir užpildytų Žulija aibių vaizdai gaunami, panaudojant "pabėgimo laiko" algoritmą. Norėdami šį algoritmą naudoti kompleksinio daugianario šaknų vizualizacijai, turime nurodyti iteracijų skaiči��, algoritmo tikslumą, žingsnį bei kompleksiniu Niutono metodu rasti daugianario šaknis. Taikant Niutono metodą, buvo susidurta su pradinių taškų parinkimo problema. Tyrimo metu patvirtinta, kad pakanka Niutono iteracinę funkciją taikyti taškams z, kurių modulis 2. Darbe buvo pasiūlytas šaknų lokalizacijos srities nustatymo būdas. Naudojant PL-algoritmą, pasirinktu žingsniu pereiname visus taškus, kurie patenka į šią sritį. Taip gauname Niutono-Rafsono fraktalus ir lygiagrečiai analizuojame Žulija aibes bei užpildytas Žulija aibes. / Julia sets and filled Julia sets of Newton‘s fractals are analyzed in this work. The Escape Time Algorithm provides us with a means for "seeing" the filled Julia sets of Newton‘s fractals, but roots, (zeros) of the polynomial under investigation should be known. The Newton‘s method for finding roots of an algebraic equation is well known. Here in the paper the complex Newton method for finding roots of a complex polynomial is presented. The main difficulties, associated with implementation of this method in practice, are discussed, namely: construction of the set of initial points (first approximations of the roots), finding the basin of attraction for a particular root and so forth. Some experimental results are presented.

Aerodynamic shape optimization and multidisciplinary optimization algorithms have the potential not only to improve conventional aircraft, but also to enable the design of novel configurations. By their very nature, these algorithms generate and analyze a large number of unique shapes, resulting in high computational costs. In order to improve their efficiency and enable their use in the early stages of the design process, a fast and robust flow solution algorithm is necessary. This thesis presents an efficient parallel Newton-Krylov-Schur flow solution algorithm for the three-dimensional Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts (SBP) operators on multi-block structured grids with simultaneous approximation terms (SATs) to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using the flexible Krylov subspace iterative method GMRES with an approximate-Schur parallel preconditioner. The algorithm is thoroughly verified and validated, highlighting the correspondence of the current algorithm with several established flow solvers. The solution for a transonic flow over a wing on a mesh of medium density (15 million nodes) shows good agreement with experimental results. Using 128 processors, deep convergence is obtained in under 90 minutes. The solution of transonic flow over the Common Research Model wing-body geometry with grids with up to 150 million nodes exhibits the expected grid convergence behavior. This case was completed as part of the Fifth AIAA Drag Prediction Workshop, with the algorithm producing solutions that compare favourably with several widely used flow solvers. The algorithm is shown to scale well on over 6000 processors. The results demonstrate the effectiveness of the SBP-SAT spatial discretization, which can be readily extended to high order, in combination with the Newton-Krylov-Schur iterative method to produce a powerful parallel algorithm for the numerical solution of the Reynolds-averaged Navier-Stokes equations. The algorithm can efficiently solve the flow over a range of clean geometries, making it suitable for use at the core of an optimization algorithm.

Aerodynamic shape optimization and multidisciplinary optimization algorithms have the potential not only to improve conventional aircraft, but also to enable the design of novel configurations. By their very nature, these algorithms generate and analyze a large number of unique shapes, resulting in high computational costs. In order to improve their efficiency and enable their use in the early stages of the design process, a fast and robust flow solution algorithm is necessary. This thesis presents an efficient parallel Newton-Krylov-Schur flow solution algorithm for the three-dimensional Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts (SBP) operators on multi-block structured grids with simultaneous approximation terms (SATs) to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using the flexible Krylov subspace iterative method GMRES with an approximate-Schur parallel preconditioner. The algorithm is thoroughly verified and validated, highlighting the correspondence of the current algorithm with several established flow solvers. The solution for a transonic flow over a wing on a mesh of medium density (15 million nodes) shows good agreement with experimental results. Using 128 processors, deep convergence is obtained in under 90 minutes. The solution of transonic flow over the Common Research Model wing-body geometry with grids with up to 150 million nodes exhibits the expected grid convergence behavior. This case was completed as part of the Fifth AIAA Drag Prediction Workshop, with the algorithm producing solutions that compare favourably with several widely used flow solvers. The algorithm is shown to scale well on over 6000 processors. The results demonstrate the effectiveness of the SBP-SAT spatial discretization, which can be readily extended to high order, in combination with the Newton-Krylov-Schur iterative method to produce a powerful parallel algorithm for the numerical solution of the Reynolds-averaged Navier-Stokes equations. The algorithm can efficiently solve the flow over a range of clean geometries, making it suitable for use at the core of an optimization algorithm.

Uncalibrated visual servoing (VS) can improve robot performance without needing camera and robot parameters. Multiple cameras improve uncalibrated VS precision, but no works exist simultaneously using more than two cameras. The first data for uncalibrated VS simultaneously using more than two cameras are presented. VS performance is also compared for two different camera models: a high-cost camera and a low-cost camera, the difference being image noise magnitude and focal length. A Kalman filter based control law for uncalibrated VS is introduced and shown to be stable under the assumptions that robot joint level servo control can reach commanded joint offsets and that the servoing path goes through at least one full column rank robot configuration. Adaptive filtering by a covariance matching technique is applied to achieve automatic camera weighting, prioritizing the best available data. A decentralized sensor fusion architecture is utilized to assure continuous servoing with camera occlusion. The decentralized adaptive Kalman filter (DAKF) control law is compared to a classical method, Gauss-Newton, via simulation and experimentation. Numerical results show that DAKF can improve average tracking error for moving targets and convergence time to static targets. DAKF reduces system sensitivity to noise and poor camera placement, yielding smaller outliers than Gauss-Newton. The DAKF system improves visual servoing performance, simplicity, and reliability.

This thesis addresses optimal control problems with elasticity for large deformations. A hyperelastic model with a polyconvex energy density is employed to describe the elastic behavior of a body. The two approaches to derive the nonlinear partial differential equation, a balance of forces and an energy minimization, are compared. Besides the conventional volume and boundary loads, two novel internal loads are presented. Furthermore, curvilinear coordinates and a hierarchical plate model can be incorporated into the formulation of the elastic forward problem. The forward problem can be solved with Newton\\\'s method, though a globalization technique should be used to avoid divergence of Newton\\\'s method. The repeated solution of the Newton system is done by a CG or MinRes method with a multigrid V-cycle as a preconditioner. The optimal control problem consists of the displacement (as the state) and a load (as the control). Besides the standard tracking-type objective, alternative objective functionals are presented for problems where a reasonable desired state cannot be provided. Two methods are proposed to solve the optimal control problem: an all-at-once approach by a Lagrange-Newton method and a reduced formulation by a quasi-Newton method with an inverse limited-memory BFGS update. The algorithms for the solution of the forward problem and the optimal control problem are implemented in the finite-element software FEniCS, with the geometrical multigrid extension FMG. Numerical experiments are performed to demonstrate the mesh independence of the algorithms and both optimization methods.