We show that a color algorithm capable of separating illumination from reflectance in a Mondrian world can be learned from a set of examples. The learned algorithm is equivalent to filtering the image data---in which reflectance and illumination are mixed---through a center-surround receptive field in individual chromatic channels. The operation resembles the "retinex" algorithm recently proposed by Edwin Land. This result is a specific instance of our earlier results that a standard regularization algorithm can be learned from examples. It illustrates that the natural constraints needed to solve a problemsin inverse optics can be extracted directly from a sufficient set of input data and the corresponding solutions. The learning procedure has been implemented as a parallel algorithm on the Connection Machine System.

abstract: Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. A full life cycle for many mechanical devices depends (i) on a wise assignment of tolerances during design and (ii) on careful quality control of the manufacturing process to ensure adherence to the specified tolerances. This thesis describes a new method for quality control of a manufacturing process by improving the method used to convert measured points on a part to a geometric entity that can be compared directly with tolerance specifications. The focus of this paper is the development of a new computational method for obtaining the least-squares fit of a set of points that have been measured with a coordinate measurement machine along a line-profile. The pseudo-inverse of a rectangular matrix is used to convert the measured points to the least-squares fit of the profile. Numerical examples are included for convex and concave line-profiles, that are formed from line- and circular arc-segments. / Dissertation/Thesis / M.S. Mechanical Engineering 2013

Assume that F is a nonlinear operator on a real Hilbert space H which is strongly monotone and Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed point sets of a finite number of nonexpansive mappings on H. We make a slight modification of the iterative algorithm in Xu and Kim (Journal of Optimization Theory and Applications, Vol. 119, No. 1, pp. 185-201, 2003), which generates a sequence {xn} from an arbitrary initial point x0 in H. The sequence {xn} is shown to converge in norm to the unique solution u* of the variational inequality, under the conditions different from Xu and Kim¡¦s ones imposed on the parameters. Applications to constrained generalized pseudoinverse are included. The results presented in this paper are complementary ones to Xu and Kim¡¦s theorems (Journal of Optimization Theory and Applications, Vol. 119, No. 1, pp. 185-201, 2003).

No description available.

The purpose of this thesis is to implement algorithms of matrix eigendecomposition and pseudoinverse computation on a Field Programmable Gate Array (FPGA) platform. Firstly, there are described matrix decomposition methods that are broadly used in mentioned algorithms. Next section is focused on the basic theory and methods of computation eigenvalues and eigenvectors as well as matrix pseudoinverse. Several examples of implementation using Matlab are attached. The Vivado High-Level Synthesis tools and libraries were used for final implementation. After the brief introduction into the FPGA fundamentals the thesis continues with a description of implemented blocks. The results of each variant were compared in terms of timing and FPGA utilization. The selected block has been validated on the development board and its arithmetic precision was analyzed.

The theoretical contents of this thesis are studies of overcomplete models. Those are the models of signals, on which is set for their parametrization more variables, than it's necessary and consequently there's computed so-called sparse solution via iteration algorithms. A goal of this analysis is a selection just of the considerable (sparse) parameters. The theory is based on a linear algebra, vector spaces, bases and so-called frames. The task of the individual project of this thesis is a description and simulation of two speech coders: a classical coder based on linear predictive speech coding and a coder, that's making use of overcomplete stochastic ARMA processes models. A part of their realization is to simulate their decoders and a analyze their reconstruction quality. For their realization there is used MATLAB and an overcomplete models' library (toolbox frames).

Cette thèse s'articule autour de deux thèmes : une transformation de B(H) introduite par Aluthge et la méthode d'Ansari-Enflo. La première partie fait l'objet de l'étude de la transformation d'Aluthge qui a eu un impact important ces dernières années en théorie des opérateurs. Des résultats optimaux sur la stabilité d'un certain nombre de classes d'opérateurs, telles que la classe des isométries partielles et les classes associées au comportement asymptotique d'un opérateur, sont fournis. Nous étudions également l'évolution d'invariants opératoriels, tels que le polynôme minimal, la fonction minimum, l'ascente et la descente, sous l'action de la transformation ; nous comparons plus précisément les suites des noyaux et images relatives aux itérés d'un opérateur et de sa transformée de Aluthge. La deuxième partie est l'occasion d'étudier la théorie d'Ansari-Enflo, qui a permis de gros progrès pour le problème du sous-espace hyper-invariant. Nous développons plus particulièrement la notion fondatrice de la méthode, celle de vecteur extrémal. La localisation et une nouvelle caractérisation de ces vecteurs sont données. Leur régularité et leur robustesse, au regard de différents paramètres, sont éprouvées. Enfin, nous comparons les vecteurs extrémaux d'un shift à poids et ceux associés à sa transformée d'Aluthge. Cette étude aboutit à la construction d'une suite de vecteurs extrémaux associés aux itérés de la transformation d'Aluthge, pour laquelle certaines propriétés sont mises en évidence.

<p>In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem can be solved by iteration, but due to complicated computations of derivatives and the existence of several local minima, so called short-cut methods may be an alternative. These methods are based on simplified versions of the original problem. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, different kinds of discretizations and formulations of the optimization problem are discussed as well as the effect of ill-conditioning.</p><p>Computation of parameters often includes as a part solution of linear system of equations <i>Ax = b</i>. The corresponding pseudoinverse solution depends on the properties of the matrix <i>A</i> and vector <i>b</i>. The singular value decomposition of <i>A</i> can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in the input data affect the solution <i>x</i>. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the effect of a more limited amount of perturbations and in that sense be more realistic. It is shown how the effect of perturbations can be analyzed by a semi-experimental analysis. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of <i>A</i> into account</p>

In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem can be solved by iteration, but due to complicated computations of derivatives and the existence of several local minima, so called short-cut methods may be an alternative. These methods are based on simplified versions of the original problem. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, different kinds of discretizations and formulations of the optimization problem are discussed as well as the effect of ill-conditioning. Computation of parameters often includes as a part solution of linear system of equations Ax = b. The corresponding pseudoinverse solution depends on the properties of the matrix A and vector b. The singular value decomposition of A can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in the input data affect the solution x. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the effect of a more limited amount of perturbations and in that sense be more realistic. It is shown how the effect of perturbations can be analyzed by a semi-experimental analysis. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of A into account

The diploma thesis deals with the topic of free-form deformations. The main goal of this work were elaboration of theoretical knowledge about this issue and the programming of selected methods od free-form deformations. The first part describes the required spline theory, matrix calculus and free-form deformations. The resulting version shows three programs. The first program compares the selected free-form deformation methods to the example of the 4x4 control point grid. The second program serves as a generalization for the general case of grid of control points. The last program is based on direct manipulation of arbitrary surface point and following recomputation of the control points to obtain demanded shape.