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Articles 138541 - 138570 of 303800

Full-Text Articles in Physical Sciences and Mathematics

Monte Carlo Simulation Of Multiple Photon Scattering In Sugar Maple Tree Canopies, Michael Greiner, Bradley Duncan, Matthew Dierking Nov 2015

Monte Carlo Simulation Of Multiple Photon Scattering In Sugar Maple Tree Canopies, Michael Greiner, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

Detecting objects hidden beneath forest canopies is a difficult task for optical remote sensing systems. Rather than relying upon the existence of gaps between leaves, as other researchers have done, our ultimate goal is to use light scattered by leaves to image through dense foliage. Herein we describe the development of a Monte Carlo model for simulating the scattering of light as it propagates through the leaves of an extended tree canopy. We measured several parameters, including the gap fraction and maximum leaf-area density, of a nearby sugar maple tree grove and applied them to our model. We report the …


Improving Mid-Frequency Contrast In Sparse Aperture Optical Imaging Systems Based Upon The Golay-9 Array, Andrew Stokes, Bradley Duncan, Matthew Dierking Nov 2015

Improving Mid-Frequency Contrast In Sparse Aperture Optical Imaging Systems Based Upon The Golay-9 Array, Andrew Stokes, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

Sparse aperture imaging systems are capable of producing high resolution images while maintaining an overall light collection area that is small compared to a fully filled aperture yielding the same resolution. This is advantageous for applications where size, volume, weight and/or cost are important considerations. However, conventional sparse aperture systems pay the penalty of reduced contrast at midband spatial frequencies. This paper will focus on increasing the midband contrast of sparse aperture imaging systems based on the Golay-9 array. This is one of a family of two-dimensional arrays we have previously examined due to their compact, non-redundant autocorrelations. The modulation …


Periodic, Pseudo-Noise Waveforms For Multi-Function Coherent Ladar, Matthew Dierking, Bradley Duncan Nov 2015

Periodic, Pseudo-Noise Waveforms For Multi-Function Coherent Ladar, Matthew Dierking, Bradley Duncan

Bradley D. Duncan

We report the use of periodic, pseudonoise waveforms in a multifunction coherent ladar system. We exploit the Doppler sensitivity of these waveforms, as well as agile processing, to enable diverse ladar functions, including high range resolution imaging, macro-Doppler imaging, synthetic aperture ladar, and range-resolved micro-Doppler imaging. We present analytic expressions and simulations demonstrating the utility of pseudonoise waveforms for each of the ladar modes. We also discuss a laboratory pseudonoise ladar system that was developed to demonstrate range compression and range-resolved micro-Doppler imaging, as well as the phase recovery common to each of the coherent modes.


Holographic Aperture Ladar, Bradley Duncan, Matthew Dierking Nov 2015

Holographic Aperture Ladar, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

Holographic aperture ladar is a variant of synthetic aperture ladar that seeks to increase cross-range scene resolution by synthesizing a large effective aperture through the motion of a smaller receiver and through the subsequent proper phasing and correlation of the detected signals in postprocessing. Unlike in conventional synthetic aperture ladar, however, holographic aperture ladar makes use of a two- dimensional translating sensor array, not simply a translating point detector. Also unlike in conventional synthetic aperture ladar, holographic aperture images will be formed in the two orthogonal cross-range dimensions parallel and perpendicular to the sensor platform’s direction of motion. The central …


Experimental Demonstration Of A Stripmap Holographic Aperture Ladar System, Jason Stafford, Bradley Duncan, Matthew Dierking Nov 2015

Experimental Demonstration Of A Stripmap Holographic Aperture Ladar System, Jason Stafford, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

By synthesizing large effective apertures through the translation of a smaller imaging sensor and the subsequent proper phasing and correlation of detected signals in postprocessing, holographic aperture ladar (HAL) systems seek to increase the resolution of remotely imaged targets. The stripmap HAL process was demonstrated in the laboratory, for the first time to our knowledge. Our results show that the stripmap HAL transformation can precisely account for off-axis transmitter induced phase migrations. This in turn allows multiple pupil plane field segments, sequentially collected across a synthetic aperture, to be coherently mosaiced together. As a direct consequence, we have been able …


Review: 'Theory Of Dielectric Optical Waveguides,' 2nd Edition, By Dietrich Marcuse, Bradley D. Duncan Nov 2015

Review: 'Theory Of Dielectric Optical Waveguides,' 2nd Edition, By Dietrich Marcuse, Bradley D. Duncan

Bradley D. Duncan

I suppose I ought to say up front that while preparing this review I often found myself feeling very much like a student evaluating his teacher. After all, it was, in part, the first edition of Dietrich Marcuse's Theory of Dielectric Optical Waveguides (among a handful of other similar texts) from which I first studied the principles of optical waveguide theory under the demanding, yet patient and graceful guidance of Dr. Ahmad Safaai-Jazi. Thus with the utmost respect for a teacher whom I have never met, I shall try to faithfully share my thoughts and feelings regarding the second edition …


Modal Interference Techniques For Strain Detection In Few-Mode Optical Fibers, Bradley D. Duncan Nov 2015

Modal Interference Techniques For Strain Detection In Few-Mode Optical Fibers, Bradley D. Duncan

Bradley D. Duncan

Interference between the modes of an optical fiber results in specific intensity patterns which can be modulated as a function of disturbances in the optical fiber system. These modulation effects are a direct result of the difference in propagation constants of the constituent modes. In this presentation it is shown how the modulated intensity patterns created by the interference of specific mode groups in few-mode optical fibers (V < 5.0) can be used to detect strain. A detailed discussion of the modal phenomena responsible for the observed strain induced pattern modulation is given and it is shown that strain detection sensitivities …


Effects Of Spatial Modes On Ladar Vibration Signature Estimation, Douglas Jameson, Matthew Dierking, Bradley Duncan Nov 2015

Effects Of Spatial Modes On Ladar Vibration Signature Estimation, Douglas Jameson, Matthew Dierking, Bradley Duncan

Bradley D. Duncan

Ladar-based vibrometry has been shown to be a powerful technique in enabling the plant identification of machines. Rather than sensing the geometric shape of a target laser vibrometers sense motions of the target induced by moving parts within the system. Since the target need not be spatially resolved, vibration can be sensed reliably and provide positive identification at ranges beyond the imaging limits of the aperture. However, as the range of observation increases, the diffraction-limited beam size on the target increases as well, and may encompass multiple vibrational modes on the target's surface. As a result, vibration estimates formed from …


Bidirectional Scattering Distribution Functions Of Maple And Cottonwood Leaves, Michael Greiner, Bradley Duncan, Matthew Dierking Nov 2015

Bidirectional Scattering Distribution Functions Of Maple And Cottonwood Leaves, Michael Greiner, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

We present our investigations into the optical scattering properties of both sugar maple (Acer saccarum) and eastern cottonwood (Populus deltoides) leaves in the near-IR wavelength regime. The bidirectional scattering distribution function (BSDF) describes the fractions of light reflected by and transmitted through a leaf for a given set of illumination and observation angles. Experiments were performed to measure the BSDF of each species at a discrete set of illumination and observation angles. We then modeled the BSDFs in such a way that other researchers may interpolate their values for scattering in any direction under illumination at any angle.


Demonstrated Resolution Enhancement Capability Of A Stripmap Holographic Aperture Ladar System, Samuel Venable, Bradley Duncan, Matthew Dierking, David Rabb Nov 2015

Demonstrated Resolution Enhancement Capability Of A Stripmap Holographic Aperture Ladar System, Samuel Venable, Bradley Duncan, Matthew Dierking, David Rabb

Bradley D. Duncan

Holographic aperture ladar (HAL) is a variant of synthetic aperture ladar (SAL). The two processes are related in that they both seek to increase cross-range (i.e., the direction of the receiver translation) image resolution through the synthesis of a large effective aperture. This is in turn achieved via the translation of a receiver aperture and the subsequent coherent phasing and correlation of multiple received signals. However, while SAL imaging incorporates a translating point detector, HAL takes advantage of a two-dimensional translating sensor array. For the research presented in this article, a side-looking stripmap HAL geometry was used to sequentially image …


Saturated Semiconductor Optical Amplifier Phase Modulation For Long Range Laser Radar Applications, Jennifer Carns, Bradley Duncan, Matthew Dierking Nov 2015

Saturated Semiconductor Optical Amplifier Phase Modulation For Long Range Laser Radar Applications, Jennifer Carns, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

We investigate the use of a semiconductor optical amplifier operated in the saturation regime as a phase modulator for long range laser radar applications. The nature of the phase and amplitude modulation resulting from a high peak power Gaussian pulse, and the impact this has on the ideal pulse response of a laser radar system, is explored. We also present results of a proof-of-concept laboratory demonstration using phase-modulated pulses to interrogate a stationary target.


Review: 'Integrated Optics: Design And Modeling,' By Reinhard Marz, Bradley D. Duncan Nov 2015

Review: 'Integrated Optics: Design And Modeling,' By Reinhard Marz, Bradley D. Duncan

Bradley D. Duncan

My overall impression is that Integrated Optics: Design and Modeling will make a fine addition to almost anyone's collection of books on integrated optics. It will, however, serve its readers better as a reference book than as a text from which to first learn the basic concepts of integrated optics. I say this because the book is written at a fairly sophisticated technical level, though the author often moves rather quickly to the "bottom line" without providing material much beyond what is first necessary to introduce a problem or concept, and then a statement of the results and/or implications. It …


Controlling Surface Chemistry Of Liquid Metals To Enhance Their Fluidic Properties, Nahid Ilyas Nov 2015

Controlling Surface Chemistry Of Liquid Metals To Enhance Their Fluidic Properties, Nahid Ilyas

Physics Seminars

Gallium liquid metal alloys (GaLMA) are one of the key components of emerging technologies in reconfigurable, flexible, and printable electronics. Surface properties of GaLMA play important roles in its application in reconfigurable devices, such as tunable radio frequency antennas and electronic swilches. Reversible flow of GaLMA in microchannels of these types of devices is hindered by the presence of an oxide skin that forms spontaneously in ambient environment. The oxide film sticks to most surfaces leaving unwanted residues behind that can cause undesired electronic properties. This presentation describes a novel method that enables the movement of gallium liquid metal alloys …


Meta-Analysis Of Genome-Wide Association Studies With Correlated Individuals: Application To The Hispanic Community Health Study/Study Of Latinos (Hchs/Sol), Tamar Sofer, John R. Shaffer, Misa Graff, Qibin Qi, Adrienne M. Stilp, Stephanie M. Gogarten, Kari E. North, Carmen R. Isasi, Cathy C. Laurie, Adam A. Szpiro Nov 2015

Meta-Analysis Of Genome-Wide Association Studies With Correlated Individuals: Application To The Hispanic Community Health Study/Study Of Latinos (Hchs/Sol), Tamar Sofer, John R. Shaffer, Misa Graff, Qibin Qi, Adrienne M. Stilp, Stephanie M. Gogarten, Kari E. North, Carmen R. Isasi, Cathy C. Laurie, Adam A. Szpiro

UW Biostatistics Working Paper Series

Investigators often meta-analyze multiple genome-wide association studies (GWASs) to increase the power to detect associations of single nucleotide polymorphisms (SNPs) with a trait. Meta-analysis is also performed within a single cohort that is stratified by, e.g., sex or ancestry group. Having correlated individuals among the strata may complicate meta-analyses, limit power, and inflate Type 1 error. For example, in the Hispanic Community Health Study/Study of Latinos (HCHS/SOL), sources of correlation include genetic relatedness, shared household, and shared community. We propose a novel mixed-effect model for meta-analysis, “MetaCor", which accounts for correlation between stratum-specific effect estimates. Simulations show that MetaCor controls …


Species Specific Microcalcification In Reef Building Caribbean Corals In Ocean Acidification Conditions, Ashley M. Dungan Nov 2015

Species Specific Microcalcification In Reef Building Caribbean Corals In Ocean Acidification Conditions, Ashley M. Dungan

HCNSO Student Theses and Dissertations

Coral reefs are one of the most economically important ecosystems on the planet. Despite their great contribution to the world economy, anthropogenic influence via carbon dioxide emissions is leading to unprecedented changes with concerns about subsequent negative impacts on reefs. Surface ocean pH has dropped 0.1 units in the past century; in spite of this rapid shift in oceanic chemistry, it is unclear if individual species or life stages of Caribbean stony corals will be more sensitive to ocean acidification (OA). Examined is the relationship between CO2-induced seawater acidification, net calcification, photosynthesis, and respiration in three model Caribbean …


A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu Nov 2015

A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu

CMC Faculty Publications and Research

Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many socalled signal space methods have been developed to extend this body of work to signals sparse in arbitrary dictionaries rather than orthonormal bases. In doing so, CS can be utilized in a much broader array of practical settings. Often, such approaches often rely on the ability to optimally project a signal onto a small number of dictionary atoms. Such optimal, or even approximate, projections have been difficult to derive theoretically. Nonetheless, it has …


High Pressure Studies Of Nanostructured Tio2 And Li4ti5o12 Using Raman Spectroscopy And Synchrotron X-Ray Radiation, Fengping Xiao Nov 2015

High Pressure Studies Of Nanostructured Tio2 And Li4ti5o12 Using Raman Spectroscopy And Synchrotron X-Ray Radiation, Fengping Xiao

Electronic Thesis and Dissertation Repository

Nanomaterials have been extensively studied due to their distinctive properties such as surface effect, small-size effect and quantum size effect. In recent year, investigations of the structural and phase transformations of nanomaterials under high pressure are receiving increasing attentions. In addition to composition and synthetic routes, pressure provides a clean way to adjust interatomic distance and hence affect the crystal structure and thus properties of the nanostructured materials.Two nanomaterials (i.e. TiO2 and Li4Ti5O12) with different morphologies are studied in this thesis.

In part I, the high-pressure behaviours of four hydrothermal synthesized 1D rutile …


Science Undergraduate Research Conference 2015 Booklet, Dublin Institute Of Technology, Institute Of Technology, Tallaght, Institute Of Technology, Blanchardstown Nov 2015

Science Undergraduate Research Conference 2015 Booklet, Dublin Institute Of Technology, Institute Of Technology, Tallaght, Institute Of Technology, Blanchardstown

Group Reports

Dublin Institute of Technology (DIT), IT Tallaght and IT Blanchardstown hosted the Science Undergraduate Research Conference (SURC 2015) on 13th November 2015 in DIT's Grangegorman Campus. 25 students from DIT, IT Tallaght and IT Blanchardstown who completed an undergraduate research project in a Scientific discipline in the academic year 2014-15 presented at this conference.

The aims of the conference were to:

  1. Provide current students with an opportunity to gain an understanding of the work which has been undertaken by recent graduates, and the career opportunities that exist for graduates in Scientific disciplines.
  2. Provide recent graduates with an opportunity to gain …


Gis-Integrated Mathematical Modeling Of Social Phenomena At Macro- And Micro- Levels—A Multivariate Geographically-Weighted Regression Model For Identifying Locations Vulnerable To Hosting Terrorist Safe-Houses: France As Case Study, Elyktra Eisman Nov 2015

Gis-Integrated Mathematical Modeling Of Social Phenomena At Macro- And Micro- Levels—A Multivariate Geographically-Weighted Regression Model For Identifying Locations Vulnerable To Hosting Terrorist Safe-Houses: France As Case Study, Elyktra Eisman

FIU Electronic Theses and Dissertations

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to …


Models Describing The Sea Level Rise In Key West, Florida, Karm-Ervin Jean Nov 2015

Models Describing The Sea Level Rise In Key West, Florida, Karm-Ervin Jean

FIU Electronic Theses and Dissertations

Lately, we have been noticing an unusual rise in the sea level near many Floridian cities. By 2060, scientists believe that the sea level in the city of Key West will reach between 22.86 to 60.96 centimeters (Strauss et al. 2012). The consequences of sea level rise are unpleasant by gradually tearing away our beaches and natural resources, destroying our homes and businesses, etc. Definitively, a continual increase of the sea level will affect everyone either directly or indirectly.

In this study, the sea level measurements of four Floridian coastal cities (including Key West) are collected in order to describe …


Online Moving Object Visualization With Geo-Referenced Data, Guangqiang Zhao Nov 2015

Online Moving Object Visualization With Geo-Referenced Data, Guangqiang Zhao

FIU Electronic Theses and Dissertations

As a result of the rapid evolution of smart mobile devices and the wide application of satellite-based positioning devices, the moving object database (MOD) has become a hot research topic in recent years. The moving objects generate a large amount of geo-referenced data in different types, such as videos, audios, images and sensor logs. In order to better analyze and utilize the data, it is useful and necessary to visualize the data on a map.

With the rise of web mapping, visualizing the moving object and geo-referenced data has never been so easy. While displaying the trajectory of a moving …


Development Of A Two-Fluid Drag Law For Clustered Particles Using Direct Numerical Simulation And Validation Through Experiments, Ahmadreza Abbasi Baharanchi Nov 2015

Development Of A Two-Fluid Drag Law For Clustered Particles Using Direct Numerical Simulation And Validation Through Experiments, Ahmadreza Abbasi Baharanchi

FIU Electronic Theses and Dissertations

This dissertation focused on development and utilization of numerical and experimental approaches to improve the CFD modeling of fluidization flow of cohesive micron size particles. The specific objectives of this research were: (1) Developing a cluster prediction mechanism applicable to Two-Fluid Modeling (TFM) of gas-solid systems (2) Developing more accurate drag models for Two-Fluid Modeling (TFM) of gas-solid fluidization flow with the presence of cohesive interparticle forces (3) using the developed model to explore the improvement of accuracy of TFM in simulation of fluidization flow of cohesive powders (4) Understanding the causes and influential factor which led to improvements and …


Critical Thinking And High-Level Discourse In A 1:1 Environment, Ryan G. Zonnefeld, Valorie L. Zonnefeld Nov 2015

Critical Thinking And High-Level Discourse In A 1:1 Environment, Ryan G. Zonnefeld, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Learn about our experiences co-teaching a K–8 methods course using 1:1 tablets in a high-tech lab. This innovative course included a move away from a textbook to a dynamic research-based curriculum supported by NCTM resources and CCSSM as well as integral utilization of apps, web 2.0 tools, and professional learning networks.


Characterization Of Physical, Spectroscopic And Thermal Properties Of Biofield Treated Biphenyl, Mahendra Kumar Trivedi, Rama Mohan Tallapragada, Alice Branton, Dahryn Trivedi, Gopal Nayak, Rakesh K. Mishra, Snehasis Jana Nov 2015

Characterization Of Physical, Spectroscopic And Thermal Properties Of Biofield Treated Biphenyl, Mahendra Kumar Trivedi, Rama Mohan Tallapragada, Alice Branton, Dahryn Trivedi, Gopal Nayak, Rakesh K. Mishra, Snehasis Jana

Mahendra Kumar Trivedi

Biphenyl is used as an intermediate for synthesis of various pharmaceutical compounds. The objective of present research was to investigate the influence of biofield treatment on physical, spectroscopic and thermal properties of biphenyl. The study was performed in two groups (control and treated). The control group remained as untreated, and biofield treatment was given to treated group. The control and treated biphenyl were characterized by X-ray diffraction (XRD), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), Fourier transform infrared (FT-IR) spectroscopy, Ultraviolet-visible (UV-Vis) spectroscopy and surface area analysis. The treated biphenyl showed decrease in intensity of XRD peaks as compared to …


Characterization Of Physical, Thermal And Spectral Properties Of Biofield Treated 2,6-Dichlorophenol, Mahendra Kumar Trivedi, Rama Mohan Tallapragada, Alice Branton, Dahryn Trivedi, Gopal Nayak, Rakesh K. Mishra, Snehasis Jana Nov 2015

Characterization Of Physical, Thermal And Spectral Properties Of Biofield Treated 2,6-Dichlorophenol, Mahendra Kumar Trivedi, Rama Mohan Tallapragada, Alice Branton, Dahryn Trivedi, Gopal Nayak, Rakesh K. Mishra, Snehasis Jana

Mahendra Kumar Trivedi

2,6-Dichlorophenol (2,6-DCP) is a compound used for the synthesis of chemicals and pharmaceutical agents. The present work is intended to evaluate the impact of Mr. Trivedi’s biofield energy treatment on physical, thermal and spectral properties of the 2,6-DCP. The control and treated 2,6-DCP were characterized by various analytical techniques such as X-ray diffraction (XRD), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), Fourier transform infrared (FT-IR) spectroscopy, and ultra violet-visible spectroscopy (UV-vis) analysis. The XRD results showed the increase in crystallite size of treated sample by 28.94% as compared to the control sample. However, the intensity of the XRD peaks of …


Match-Making For Stability: A Survey Of The Stable Marriage Problem, Adam J. Hammett Nov 2015

Match-Making For Stability: A Survey Of The Stable Marriage Problem, Adam J. Hammett

Mathematics Colloquium

No abstract provided.


Cosmic Radiation, Anthony Keane Nov 2015

Cosmic Radiation, Anthony Keane

The ITB Journal

The planet Earth orbits the Sun in what is often considered to be empty space but is in fact full of very small charged particles speeding in all directions. The situation can be compared to the Earth having to constantly travel in a light shower of rain and with the atmosphere acting like an umbrella. The 'rain' is made up of charged particles called 'Cosmic Rays'. The name cosmic ray was given long ago to invisible ionising radiation that could mysteriously discharge an electroscope even when the electroscope was heavy insulated. Early scientists quickly established a relationship between the rate …


The Firece Green Fire: Vol. 6 Issue 10, Wofford College Environmental Studies Program Nov 2015

The Firece Green Fire: Vol. 6 Issue 10, Wofford College Environmental Studies Program

The Fierce Green Fire

No abstract provided.


Energy Dependence Of Acceptance-Corrected Dielectron Excess Mass Spectrum At Mid-Rapidity In Au + Au Collisions At √SNn = 19.6 And 200 Gev, James K. Adkins, Renee H. Fatemi, Suvarna Ramachandran, L. Adamczyk, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, A. Aparin, D. Arkhipkin, E. C. Aschenauer, G. S. Averichev Nov 2015

Energy Dependence Of Acceptance-Corrected Dielectron Excess Mass Spectrum At Mid-Rapidity In Au + Au Collisions At √SNn = 19.6 And 200 Gev, James K. Adkins, Renee H. Fatemi, Suvarna Ramachandran, L. Adamczyk, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, A. Aparin, D. Arkhipkin, E. C. Aschenauer, G. S. Averichev

Physics and Astronomy Faculty Publications

The acceptance-corrected dielectron excess mass spectra, where the known hadronic sources have been subtracted from the inclusive dielectron mass spectra, are reported for the first time at mid-rapidity ∣yee∣+ Au collisions at √sNN = 19.6 and 200 GeV. The excess mass spectra are consistently described by a model calculation with a broadened ρ spectral function for Mee < 1.1 GeV/c2. The integrated dielectron excess yield at √sNN = 19.6 GeV for 0.4 < Mee < 0.75 GeV/c2, normalized to the charged particle multiplicity at mid-rapidity, has a value similar to that in ln+ln collisions at …


Convergence Properties Of The Randomized Extended Gauss-Seidel And Kaczmarz Methods, Anna Ma, Deanna Needell, Aaditya Ramdas Nov 2015

Convergence Properties Of The Randomized Extended Gauss-Seidel And Kaczmarz Methods, Anna Ma, Deanna Needell, Aaditya Ramdas

CMC Faculty Publications and Research

The Kaczmarz and Gauss-Seidel methods both solve a linear system Xβ=y by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows the randomized Kaczmarz method converges linearly in expectation to the solution. Lewis and Leventhal then proved a similar result for the randomized Gauss-Seidel algorithm. However, the behavior of both methods depends heavily on whether the system is under or overdetermined, and whether it is consistent or not. Here we provide a unified theory of both methods, their variants for these different settings, and draw connections between …