Spelling suggestions: "subject:"iterative methods (amathematics)"" "subject:"iterative methods (bmathematics)""
41 
Highdimensional Asymptotics for Phase Retrieval with Structured Sensing MatricesDudeja, Rishabh January 2021 (has links)
Phase Retrieval is an inference problem where one seeks to recover an unknown complexvalued 𝓃dimensional signal vector from the magnitudes of 𝓶 linear measurements. The linear measurements are specified using a 𝓶 × 𝓃 sensing matrix. This problem is a mathematical model for imaging systems arising in Xray crystallography and other applications where it is infeasible to acquire the phase of the measurements. This dissertation presents some results regarding the analysis of this problem in the highdimensional asymptotic regime where the number of measurements and the signal dimension diverge proportionally so that their ratio remains fixed. A limitation of existing highdimensional analyses of this problem is that they model the sensing matrix as a random matrix with independent and identically (i.i.d.) distributed Gaussian entries. In practice, this matrix is highly structured with limited randomness.
This work studies a correction to the i.i.d. Gaussian sensing model, known as the subsampled Haar sensing model which faithfully captures a crucial orthogonality property of realistic sensing matrices. The first result of this thesis provides a precise asymptotic characterization of the performance of commonly used spectral estimators for phase retrieval in the subsampled Haar sensing model. This result can be leveraged to tune certain parameters involved in the spectral estimator optimally.
The second part of this dissertation studies the informationtheoretic limits for betterthanrandom (or weak) recovery in the subsampled Haar sensing model. The main result in this part shows that appropriately tuned spectral methods achieve weak recovery with the informationtheoretically optimal number of measurements. Simulations indicate that the performance curves derived for the subsampled Haar sensing model accurately describe the empirical performance curves for realistic sensing matrices such as randomly subsampled Fourier sensing matrices and Coded Diffraction Pattern (CDP) sensing matrices. The final part of this dissertation tries to provide a mathematical understanding of this empirical universality phenomenon: For the realvalued version of the phase retrieval problem, the main result of the final part proves that the dynamics of a class of iterative algorithms, called Linearized Approximate Message Passing schemes, are asymptotically identical in the subsampled Haar sensing model and a realvalued analog of the subsampled Fourier sensing model.

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Towards optimal solution techniques for large eigenproblems in structural mechanicsRamaswamy, Seshadri. January 1980 (has links)
Thesis (Sc.D.)Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1980. / Includes bibliographical references. / by Seshadri Ramaswamy. / Thesis (Sc.D.)Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1980.

43 
Cycletocycle control of plastic sheet heating on the AAA thermoforming machineYang, Shuonan, 1984 January 2008 (has links)
No description available.

44 
Terminal iterative learning for cycletocycle control of industrial processesGauthier, Guy, 1960 January 2008 (has links)
No description available.

45 
Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's methodChoi, Yanyu., 蔡欣榆. January 2006 (has links)
published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

46 
Examples and Applications of Infinite Iterated Function SystemsHanus, Pawel Grzegorz 08 1900 (has links)
The aim of this work is the study of infinite conformal iterated function systems. More specifically, we investigate some properties of a limit set J associated to such system, its Hausdorff and packing measure and Hausdorff dimension. We provide necessary and sufficient conditions for such systems to be biLipschitz equivalent. We use the concept of scaling functions to obtain some result about 1dimensional systems. We discuss particular examples of infinite iterated function systems derived from complex continued fraction expansions with restricted entries. Each system is obtained from an infinite number of contractions. We show that under certain conditions the limit sets of such systems possess zero Hausdorff measure and positive finite packing measure. We include an algorithm for an approximation of the Hausdorff dimension of limit sets. One numerical result is presented. In this thesis we also explore the concept of positively recurrent function. We use iterated function systems to construct a natural, wide class of such functions that have strong ergodic properties.

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Symmetries and conservation laws of difference and iterative equationsFollyGbetoula, Mensah Kekeli 22 January 2016 (has links)
A thesis submitted to the Faculty of Science, University of the Witwatersrand,
Johannesburg, in ful lment of the requirements for the degree of Doctor of Philosophy.
Johannesburg, August 2015. / We construct, using rst principles, a number of nontrivial conservation
laws of some partial di erence equations, viz, the discrete Liouville equation
and the discrete SineGordon equation. Symmetries and the more recent
ideas and notions of characteristics (multipliers) for di erence equations are
also discussed.
We then determine the symmetry generators of some ordinary di erence
equations and proceed to nd the rst integral and reduce the order of the
di erence equations. We show that, in some cases, the symmetry generator
and rst integral are associated via the `invariance condition'. That is,
the rst integral may be invariant under the symmetry of the original di erence
equation. We proceed to carry out double reduction of the di erence
equation in these cases.
We then consider discrete versions of the Painlev e equations. We assume
that the characteristics depend on n and un only and we obtain a number
of symmetries. These symmetries are used to construct exact solutions in
some cases.
Finally, we discuss symmetries of linear iterative equations and their transformation
properties. We characterize coe cients of linear iterative equations
for order less than or equal to ten, although our approach of characterization
is valid for any order. Furthermore, a list of coe cients of linear iterative
equations of order up to 10, in normal reduced form is given.

48 
Applying image processing techniques to pose estimation and view synthesis.January 1999 (has links)
Fung Yiufai Phineas. / Thesis (M.Phil.)Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 142148). / Abstracts in English and Chinese. / Chapter 1  Introduction  p.1 / Chapter 1.1  Modelbased Pose Estimation  p.3 / Chapter 1.1.1  Application  3D Motion Tracking  p.4 / Chapter 1.2  Imagebased View Synthesis  p.4 / Chapter 1.3  Thesis Contribution  p.7 / Chapter 1.4  Thesis Outline  p.8 / Chapter 2  General Background  p.9 / Chapter 2.1  Notations  p.9 / Chapter 2.2  Camera Models  p.10 / Chapter 2.2.1  Generic Camera Model  p.10 / Chapter 2.2.2  Fullperspective Camera Model  p.11 / Chapter 2.2.3  Affine Camera Model  p.12 / Chapter 2.2.4  Weakperspective Camera Model  p.13 / Chapter 2.2.5  Paraperspective Camera Model  p.14 / Chapter 2.3  Modelbased Motion Analysis  p.15 / Chapter 2.3.1  Point Correspondences  p.16 / Chapter 2.3.2  Line Correspondences  p.18 / Chapter 2.3.3  Angle Correspondences  p.19 / Chapter 2.4  Panoramic Representation  p.20 / Chapter 2.4.1  Static Mosaic  p.21 / Chapter 2.4.2  Dynamic Mosaic  p.22 / Chapter 2.4.3  Temporal Pyramid  p.23 / Chapter 2.4.4  Spatial Pyramid  p.23 / Chapter 2.5  Image Preprocessing  p.24 / Chapter 2.5.1  Feature Extraction  p.24 / Chapter 2.5.2  Spatial Filtering  p.27 / Chapter 2.5.3  Local Enhancement  p.31 / Chapter 2.5.4  Dynamic Range Stretching or Compression  p.32 / Chapter 2.5.5  YIQ Color Model  p.33 / Chapter 3  Modelbased Pose Estimation  p.35 / Chapter 3.1  Previous Work  p.35 / Chapter 3.1.1  Estimation from Established Correspondences  p.36 / Chapter 3.1.2  Direct Estimation from Image Intensities  p.49 / Chapter 3.1.3  Perspective3Point Problem  p.51 / Chapter 3.2  Our Iterative P3P Algorithm  p.58 / Chapter 3.2.1  GaussNewton Method  p.60 / Chapter 3.2.2  Dealing with Ambiguity  p.61 / Chapter 3.2.3  3Dto3D Motion Estimation  p.66 / Chapter 3.3  Experimental Results  p.68 / Chapter 3.3.1  Synthetic Data  p.68 / Chapter 3.3.2  Real Images  p.72 / Chapter 3.4  Discussions  p.73 / Chapter 4  Panoramic View Analysis  p.76 / Chapter 4.1  Advanced Mosaic Representation  p.76 / Chapter 4.1.1  Frame Alignment Policy  p.77 / Chapter 4.1.2  Multiresolution Representation  p.77 / Chapter 4.1.3  Parallaxbased Representation  p.78 / Chapter 4.1.4  Multiple Moving Objects  p.79 / Chapter 4.1.5  Layers and Tiles  p.79 / Chapter 4.2  Panorama Construction  p.79 / Chapter 4.2.1  Image Acquisition  p.80 / Chapter 4.2.2  Image Alignment  p.82 / Chapter 4.2.3  Image Integration  p.88 / Chapter 4.2.4  Significant Residual Estimation  p.89 / Chapter 4.3  Advanced Alignment Algorithms  p.90 / Chapter 4.3.1  Patchbased Alignment  p.91 / Chapter 4.3.2  Global Alignment (Block Adjustment)  p.92 / Chapter 4.3.3  Local Alignment (Deghosting)  p.93 / Chapter 4.4  Mosaic Application  p.94 / Chapter 4.4.1  Visualization Tool  p.94 / Chapter 4.4.2  Video Manipulation  p.95 / Chapter 4.5  Experimental Results  p.96 / Chapter 5  Panoramic Walkthrough  p.99 / Chapter 5.1  Problem Statement and Notations  p.100 / Chapter 5.2  Previous Work  p.101 / Chapter 5.2.1  3D Modeling and Rendering  p.102 / Chapter 5.2.2  Branching Movies  p.103 / Chapter 5.2.3  Texture Window Scaling  p.104 / Chapter 5.2.4  Problems with Simple Texture Window Scaling  p.105 / Chapter 5.3  Our Walkthrough Approach  p.106 / Chapter 5.3.1  Cylindrical Projection onto Image Plane  p.106 / Chapter 5.3.2  Generating Intermediate Frames  p.108 / Chapter 5.3.3  Occlusion Handling  p.114 / Chapter 5.4  Experimental Results  p.116 / Chapter 5.5  Discussions  p.116 / Chapter 6  Conclusion  p.121 / Chapter A  Formulation of Fischler and Bolles' Method for P3P Problems  p.123 / Chapter B  Derivation of z1 and z3 in terms of z2  p.127 / Chapter C  Derivation of e1 and e2  p.129 / Chapter D  Derivation of the Update Rule for GaussNewton Method  p.130 / Chapter E  Proof of (λ1λ2λ 4）>〉0  p.132 / Chapter F  Derivation of φ and hi  p.133 / Chapter G  Derivation of w1j to w4j  p.134 / Chapter H  More Experimental Results on Panoramic Stitching Algorithms  p.138 / Bibliography  p.148

49 
Performance analysis of iterative matching scheduling algorithms in ATM inputbuffered switches.January 1999 (has links)
by Cheng Sze Wan. / Thesis (M.Phil.)Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 72[76]). / Abstracts in English and Chinese. / Chapter 1  Introduction  p.1 / Chapter 1.1  Background  p.1 / Chapter 1.2  Traffic Scheduling in Inputbuffered Switches .。  p.3 / Chapter 1.3  Organization of Thesis  p.7 / Chapter 2  Principle of Enchanced PIM Algorithm  p.8 / Chapter 2.1  Introduction  p.8 / Chapter 2.1.1  Switch Model  p.9 / Chapter 2.2  Enhanced Parallel Iterative Matching Algorithm (EPIM)  p.10 / Chapter 2.2.1  Motivation  p.10 / Chapter 2.2.2  Algorithm  p.12 / Chapter 2.3  Performance Evaluation  p.16 / Chapter 2.3.1  Simulation  p.16 / Chapter 2.3.2  Delay Analysis  p.18 / Chapter 3  Providing Bandwidth Guarantee in InputBuffered Switches  p.25 / Chapter 3.1  Introduction  p.25 / Chapter 3.2  Bandwidth Reservation in Static Scheduling Algorithm  p.26 / Chapter 3.3  Incorporation of Dynamic and Static Scheduling Algorithms .。  p.32 / Chapter 3.4  Simulation  p.34 / Chapter 3.4.1  Switch Model  p.35 / Chapter 3.4.2  Simulation Results  p.36 / Chapter 3.5  Comparison with Existing Schemes  p.42 / Chapter 3.5.1  Statistical Matching  p.42 / Chapter 3.5.2  Weighted Probabilistic Iterative Matching  p.45 / Chapter 4  EPIM and CrossPath Switch  p.50 / Chapter 4.1  Introduction  p.50 / Chapter 4.2  Concept of CrossPath Switching  p.51 / Chapter 4.2.1  Principle  p.51 / Chapter 4.2.2  Supporting Performance Guarantee in CrossPath Switch  p.52 / Chapter 4.3  Implication of EPIM on CrossPath switch  p.55 / Chapter 4.3.1  Problem Redefinition  p.55 / Chapter 4.3.2  Scheduling in Input Modules with EPIM  p.58 / Chapter 4.4  Simulation  p.63 / Chapter 5  Conclusion  p.70 / Bibliography  p.72

50 
Cyclic probabilistic reasoning networks: some exactly solvable iterative errorcontrol structures.January 2001 (has links)
Waishing Lee. / Thesis (M.Phil.)Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 114). / Abstracts in English and Chinese. / Contents  p.i / List of Figures  p.iv / List of Tables  p.v / Abstract  p.vi / Acknowledgement  p.vii / Chapter Chapter 1.  Layout of the thesis  p.1 / Chapter Chapter 2.  Introduction  p.3 / Chapter 2.1  What is the reasoning problem?  p.3 / Chapter 2.2  Fundamental nature of Knowledge  p.4 / Chapter 2.3  Fundamental methodology of Reasoning  p.7 / Chapter 2.4  Our intended approach  p.9 / Chapter Chapter 3.  Probabilistic reasoning networks  p.11 / Chapter 3.1  Overview  p.11 / Chapter 3.2  Causality and influence diagrams  p.11 / Chapter 3.3  Bayesian networks  influence diagrams endowed with a probability interpretation  p.13 / Chapter 3.3.1  A detour to the interpretations of probability  p.13 / Chapter 3.3.2  Bayesian networks  p.15 / Chapter 3.3.3  Acyclicity and global probability  p.17 / Chapter 3.4  Reasoning on probabilistic reasoning networks I  local updating formulae  p.17 / Chapter 3.4.1  Rationale of the intended reasoning strategy  p.18 / Chapter 3.4.2  Construction of the local updating formula  p.19 / Chapter 3.5  Cluster graphs  another perspective to reasoning problems  p.23 / Chapter 3.6  Semilattices  another representation of Cluster graphs  p.26 / Chapter 3.6.1  Construction of semilattices  p.26 / Chapter 3.7  Bayesian networks and semilattices  p.28 / Chapter 3.7.1  Bayesian networks to acyclic semilattices  p.29 / Chapter 3.8  Reasoning on (acyclic) probabilistic reasoning networks II  global updating schedules  p.29 / Chapter 3.9  Conclusion  p.30 / Chapter Chapter 4.  Cyclic reasoning networks  a possibility?  p.32 / Chapter 4.1  Overview  p.32 / Chapter 4.2  A meaningful cyclic structure  derivation of the ideal gas law  p.32 / Chapter 4.3  "What's ""wrong"" to be in a cyclic world"  p.35 / Chapter 4.4  Communication  Dynamics  Complexity  p.39 / Chapter 4.4.1  Communication as dynamics; dynamics to complexity  p.42 / Chapter 4.5  Conclusion  p.42 / Chapter Chapter 5.  Cyclic reasoning networks ´ؤ errorcontrol application  p.43 / Chapter 5.1  Overview  p.43 / Chapter 5.2  Communication schemes on cyclic reasoning networks directed to errorcontrol applications  p.43 / Chapter 5.2.1  Part I ´ؤ Local updating formulae  p.44 / Chapter 5.2.2  Part II  Global updating schedules across the network  p.46 / Chapter 5.3  Probabilistic reasoning based errorcontrol schemes  p.47 / Chapter 5.3.1  Local subuniverses and global universe underlying the error control structure  p.47 / Chapter 5.4  Errorcontrol structure I  p.48 / Chapter 5.4.1  Decoding algorithm  Communication between local sub universes in compliance with the global topology  p.51 / Chapter 5.4.2  Decoding rationales  p.55 / Chapter 5.4.3  Computational results  p.55 / Chapter 5.5  Errorcontrol structure II  p.57 / Chapter 5.5.1  Structure of the code and the corresponding decoding algorithm  p.57 / Chapter 5.5.2  Computational results  p.63 / Chapter 5.6  Errorcontrol structure III  p.66 / Chapter 5.6.1  Computational results  p.70 / Chapter 5.7  Errorcontrol structure IV  p.71 / Chapter 5.7.1  Computational results  p.73 / Chapter 5.8  Conclusion  p.74 / Chapter Chapter 6.  Dynamics on cyclic probabilistic reasoning networks  p.75 / Chapter 6.1  Overview  p.75 / Chapter 6.2  Decoding rationales  p.76 / Chapter 6.3  Errorcontrol structure I  exact solutions  p.77 / Chapter 6.3.1  Dynamical invariant  a key to tackle many dynamical problems  p.77 / Chapter 6.3.2  Dynamical invariant for errorcontrol structure I  p.78 / Chapter 6.3.3  Iteration dynamics  p.79 / Chapter 6.3.4  Structure preserving property and the maximum a posteriori solutions  p.86 / Chapter 6.4  Errorcontrol structures III & IV  exact solutions  p.92 / Chapter 6.4.1  Errorcontrol structure III  p.92 / Chapter 6.4.1.1  Dynamical invariants for errorcontrol structure III  p.92 / Chapter 6.4.1.2  Iteration dynamics  p.93 / Chapter 6.4.2  Errorcontrol structure IV  p.96 / Chapter 6.4.3  Structure preserving property and the maximum a posteriori solutions  p.98 / Chapter 6.5  Errorcontrol structure II  exact solutions  p.101 / Chapter 6.5.1  Iteration dynamics  p.102 / Chapter 6.5.2  Structure preserving property and the maximum a posteriori solutions  p.105 / Chapter 6.6  A comparison on the four errorcontrol structures  p.106 / Chapter 6.7  Conclusion  p.108 / Chapter Chapter 7.  Conclusion  p.109 / Chapter 7.1  Our thesis  p.109 / Chapter 7.2  Hindsights and foresights  p.110 / Chapter 7.3  Concluding remark  p.111 / Appendix A. An alternative derivation of the local updating formula  p.112 / Bibliography  p.114

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