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Course: CS 515, Fall 2008
School: Purdue
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Word Count: 1962

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8 Chapter KRYLOV SUBSPACE METHODS A more readable reference is the book by Lloyd N. Trefethen and David Bau. 8.1 Krylov Subspaces 8.2 Arnoldi Orthogonalization 8.3 Generalized Minimal Residual Method 8.4 Conjugate Gradient Method 8.5 Biconjugate Gradient Method 8.6 Biconjugate Gradient Stabilized Method 8.1 Krylov Subspaces Saad, Sections 6.1, 6.2 omitting Proposition 6.3 In a Krylov subspace method xi x0 Ki...

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8 Chapter KRYLOV SUBSPACE METHODS A more readable reference is the book by Lloyd N. Trefethen and David Bau. 8.1 Krylov Subspaces 8.2 Arnoldi Orthogonalization 8.3 Generalized Minimal Residual Method 8.4 Conjugate Gradient Method 8.5 Biconjugate Gradient Method 8.6 Biconjugate Gradient Stabilized Method 8.1 Krylov Subspaces Saad, Sections 6.1, 6.2 omitting Proposition 6.3 In a Krylov subspace method xi x0 Ki (A, r0 ) = span {r0 , Ar0 , . . . , Ai1 r0 }. We call Ki (A, r0 ) a Krylov subspace. Equivalently, xi x0 + span {r0 , Ar0 , . . . , Ai1 r0 }, which we call a linear manifold. The exact solution A1 b = x0 + A1 r0 . The minimal polynomial of A is the polynomial p(x) = xm + cm1 xm1 + + c1 x + c0 of lowest degree m such that p(A) = 0. If A is diagonalizable, m is the number of distinct eigenvalues. To see this, let A have distinct eigenvalues 1 , 2 , . . . , m , and dene p() = ( 1 )( 2 ) ( m ) = cm m + + c1 + c0 . 167 Writing A = XX 1 , we have p(A) = X( 1 I)( 2 I) ( m I)X 1 = 0. If A has is no eigenvalue equal to zero, A1 is a linear combination of I, A, . . . , Am1 , 1 1 1 1 = 3 1 . 1 1 1 e.g., 2...
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Purdue - CS - 515
Chapter 9 PRECONDITIONING9.1 Preconditioned Krylov Subspace Methods 9.2 Preconditioned Conjugate Gradient 9.3 Preconditioned Generalized Minimal Residual 9.4 Relaxation Method Preconditioners 9.5 Incomplete LU Factorization Preconditioners 9.6 Appro
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006ASSIGNMENT # 1 (30 points)January 18Due Friday, January 27 in class 0. Look over Sections 1.11.4 of the class notes and Sections 1.11.6 and 1.13 of the textbook. As a general rule, for prob
Purdue - CS - 515
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006ASSIGNMENT # 1 (30 points maximum) solutionsJanuary 301. (2 points) Assuming that A is nonsingular, prove that (A1 )T = (AT )1 . Organize your proof logically. Hence, the notation AT may be
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006ASSIGNMENT # 2 (30 points)January 27Announcements The rst examination is Wednesday, February 15 in class (from 12:30 pm to 1:20 pm). It is a closed book exam, and only pens, pencils, and e
Purdue - CS - 515
\documentclass[11pt]{article} \usepackage{fullpage,amsmath} \newcommand{\T}{^{\mathsf{T} % matrix transposition \begin{document} \begin{center} {\Large COMPUTER SCIENCE 515}\ {\Large Numerical Linear Algebra} \ {\large SPRING 2006} \ ASSIGNMENT \# 2
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006ASSIGNMENT # 2 (30 points)January 27Due Friday, February 10 in class 0. Look over Sections 1.52.5 of the class notes and Section 1.11 of the textbook. 1. (15 points) Write a recursive progr
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006ASSIGNMENT # 3 (25 points)February 10Due Friday, February 24 in class 0. Look over Chapter 3 of the class notes and Sections 1.7 and 1.12 of the textbook. 1. (5 points) Construct the orthog
Purdue - CS - 515
\documentclass[11pt]{article} \usepackage{fullpage,amsmath} \newcommand{\T}{^{\mathsf{T} % matrix transposition \begin{document} \begin{center} {\Large COMPUTER SCIENCE 515}\ {\Large Numerical Linear Algebra} \ {\large SPRING 2006} \ ASSIGNMENT \# 3
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006ASSIGNMENT # 3 (25 points)February 10Due Friday, February 24 in class 1. (5 points) Construct the orthogonal projector onto the plane through (0,0,0), (1,1,0), (1,0,1). 1 1 This plane ha
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006ASSIGNMENT # 4 (39 points)February 27Announcements The second examination is Wednesday, March 22 in class (from 12:30 pm to 1:20 pm). It is a closed book exam, and only pens, pencils, and
Purdue - CS - 515
\documentclass[11pt]{article} \usepackage{fullpage,amsmath,amssymb} \newcommand{\T}{^{\mathsf{T} % matrix transposition \begin{document} \begin{center} {\Large COMPUTER SCIENCE 515}\ {\Large Numerical Linear Algebra} \ {\large SPRING 2006} \ ASSIGNME
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006ASSIGNMENT # 4 (39 points)February 27Due Friday, March 10 in class 1. (22 points) The goal is to compare the eectiveness of ve dierent techniques for orthogonalizing the columns of a matrix
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006March 10ASSIGNMENT # 5 (17 points)Due Friday, March 31 in class 0. Look over Sections 5.1 and 5.36.2 of the class notes and Section 3.2.1, Section 3.3.2, pp. 82 84, Section 3.4, Section 3.
Purdue - CS - 515
\documentclass[11pt]{article} \usepackage{fullpage,amsmath} \usepackage[dvips]{graphicx} \newcommand{\T}{^{\mathsf{T} % matrix transposition \begin{document} \begin{center} {\Large COMPUTER SCIENCE 515}\ {\Large Numerical Linear Algebra} \ {\large SP
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006March 31ASSIGNMENT # 5 SOLUTIONS (17 points)Due Friday, March 31 in class 1. (4 points) Complete the following algorithm for performing Gaussian elimination with partial pivoting on a trid
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006March 29ASSIGNMENT # 6 (39 points)Announcements The third examination is Wednesday, April 19 in class (from 12:30 pm to 1:20 pm). It is a closed book exam, and only pens, pencils, and era
Purdue - CS - 515
\documentclass[11pt]{article} \usepackage{fullpage,amsmath,amssymb} \usepackage[dvips]{graphicx} \newcommand{\T}{^{\mathsf{T} % matrix transposition \begin{document} \begin{center} {\Large COMPUTER SCIENCE 515}\ {\Large Numerical Linear Algebra} \ {\
Purdue - CS - 515
COMPUTER SCIENCE 515 Numerical Linear AlgebraSPRING 2006Solution of Assignment # 6 (39 points)April 17Due Friday, April 14 in class 1. (20 points) The goal is to write a routine to nd roots of a polynomial using Rayleigh quotient iteration. You
Purdue - CS - 501
COMPUTER SCIENCE 501/590C Computing for Science and EngineeringFALL 2008TENTATIVE ASSIGNMENT # 2 (32 points)September 5Due Saturday, September 27 at 6:00 am Eastern Time Section 4.2 of the class notes.This assignment covers through1. (7 poi
Purdue - CS - 501
COMPUTER SCIENCE 501 Computing for Science and EngineeringFALL 2008COURSE INFORMATIONAugust 29CS 590C:See page 4 for modications pertaining to CS 590C.Course description: Computational concepts, tools, and skills for computational science an
Purdue - CS - 501
COMPUTING FOR SCIENCE AND ENGINEERINGCOPYRIGHT c 2008 Robert D. Skeel. All Rights Reserved.Contents1 Introduction 1.1 Nature of Computational Science and Engineering 1.2 Approximation . . . . . . . . . . . . . . . . . . . . 1.3 Error Propagation
Purdue - CS - 501
COMPUTER SCIENCE 501/590C Computing for Science and EngineeringFALL 2008ASSIGNMENT # 1 (32 points)September 1Due Saturday, September 13 at 6:00 am Eastern Time This assignment covers through Section 3.1 of the class notes. The rst question exerc
Purdue - CS - 501
COMPUTING FOR SCIENCE AND ENGINEERINGCOPYRIGHT c 2007 Robert D. Skeel. All Rights Reserved.Contents1 Introduction 1.1 Nature of Computational Science and Engineering 1.2 Approximation . . . . . . . . . . . . . . . . . . . . 1.3 Error Propagation
Purdue - CYTO - 1
Lecture 1First Lecture: (3rd year students) Phagocytic Cells and their function This lecture will discuss the principles of phagocytosis and neutrophil function. We will discuss the basic principles of how phagocytic cells function to bind, ingest a
Purdue - CYTO - 1
Lecture 2Clinical Applications of Flow Cytometry This lecture will discuss the current applications of flow cytometry in the clinical environment. Many of these methods are not yet applicable in veterinary medicine because of cost and development of
Purdue - CYTO - 1
The University and the High School: Scientists Participating in Education at all LevelsJ.Paul Robinson Professor of Immunopharmacology Professor of Biomedical Engineering Purdue UniversityEmail: jpr@flowcyt.cyto.purdue.edu WEB: http:/www.cyto.purdu
Purdue - CES - 06
Purdue Extension-Marion County 6640 Intech Blvd., Suite 120 Indianapolis, IN 46278-2012 Phone: (317) 275-9305 Fax (317) 275-9309Master Gardener Activity Report 2008Name: _ Telephone (day &amp; evening): __ Street Address: _ City: _, IN _ MG Class Numb
Purdue - CES - 11
Directions to Purdue Extension-Marion County6640 Intech Blvd., Suite 120, (Intech Building Ten), Indianapolis, IN 46278-2012The Purdue Extension-Marion County office is located in NW Marion County. Take the 71st Street exit from I-465. Turn west o
Purdue - CES - 11
AREA AMENITIES MAPArea Amenities3 11 10 9218 7 6 5 4 12 15 786th Street Conarroe Road Restaurants28. Burger King 1. Subway 2. Chinese Restaurant 29. Los Rancheros 3. Wendys 30. Fazolis Sub Oven 4. Romanos Macaroni Grill 31. Wendys 32. Max &amp; Ermas
Purdue - CES - 11
Master Gardener Class #2009-1 ScheduleThe first series of Master Gardener classes in 2009 will be held on Thursdays, 1:00-4:00pm, from January 8 May 21, 2009. The 18-session program will be held once a week for three hours (except where noted) at t
Purdue - CES - 11
Master Gardener Class #2009-2 ScheduleThe second series of Master Gardener classes in 2009 will be held on Thursdays, 6:00 - 9:00pm, from January 8 May 21, 2009. The 18-session program will be held once a week for three hours (except where noted) a
Purdue - M - 1
VeryIDX Transaction History based Trust establishmentJ. Woo A.Bhargav-Spantzel E. Bertino Purdue University, Department of Computer ScienceIntroduction: Increasing requirements of establishing mutual trust between user and service providers exist
Purdue - AS - 527
AS-527Department of Animal Sciencespoultry3. Partial-house brooding. Partial-house brooding is much like whole house brooding, because the total brooding area is warmed. To save energy, however, the brooding area is reduced to the minimum amount
Purdue - AGCOM - 1
NSIF-FS1Fact Sheet Number 1The Economic Impact of Genetic ImprovementIntroductionIf the pork industry in the United States is to prosper, it is imperative that production efficiency of lean, quality, consumer-oriented pork products improve. The
Purdue - AGCOM - 5
NSIF-FS5Fact Sheet Number 5Performance Records and Their Use in Genetic ImprovementIntroductionRecording performance data is common place within many swine businesses in the United States. Information such as sow farrowing and weaning data and
Purdue - AGCOM - 7
NSIF-FS7Fact Sheet Number 7Performance Records on RelativesEstimating the genetic merit of all individuals in a herd is required before a comprehensive selection and genetic improvement program can be successful. Performance records need to be c
Purdue - AGCOM - 10
NSIF-FS10Fact Sheet Number 10Multiple Trait Selection for Pork ImprovementIntroductionOne of the most important decisions breeders make is choosing which traits to improve in their herds. Breeders must decide among numerous traits of economic i
Purdue - CES - 07
Purdue extensionEC-130-WAgriculturalFarm ManagementECONOMICSIndiana Custom Rates 2007Craig L. Dobbins, Purdue Extension Economist Greg Matli, Deputy State Statistician The rates reported in this publication are based on 251 survey results re
Purdue - CES - 07
PURDUE AGRICULTURAL ECONOMICS REPORTCraig L. Dobbins, Professor and Kim Cook, Research Associate hat a difference a year can make. Last year at this time, there were questions about whether or not farmland values were nearing a top. There are no suc
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PURDUE EXTENSIONEC-713AgriculturalLegal AffairsECONOMICSLegal Aspects of Indiana Farmland Leases and Federal Tax ConsiderationsGerald A. Harrison Purdue Extension EconomistIntroductionWhen there is dissatisfaction with a lease, problems m
Purdue - CES - 07
EC-257-WAgriculturalECONOMICSFarm ManagementIndiana Cash Farm LeaseCraig L. Dobbins and J. H. Atkinson, Extension Economists Department of Agricultural Economics Purdue UniversityIntroductionA written cash farm lease agreement serves two fu
Purdue - CES - 07
INDIANA FARM LAND USE HISTORY Porter County, IndianaTotal Land Area 1997 - 267,660 AcresLand Year 1900 1910 1920 1930 1940 1950 1959 1964 1969 1974 1978 1982 1987 1992 1997 in Farms 238,783 239,329 233,828 208,406 212,937 211,471 206,571 190,448 17
Purdue - CES - 07
INDIANA CORN COUNTY LEVEL DATA2006 County Planted Acres Harvested Acres County Yield Bu/Ac 147 165 153 167 152 164 1/ 174 154 138 152 165 1/ 153 144 164 147 154 147 158 155 1/ 163 154 148 164 159 144 166 155 142 155 157 166 157 135 159 134 1/ 143 15
Purdue - CES - 07
INDIANA SOYBEAN COUNTY LEVEL DATA2006 County Planted Acres Harvested Acres County Yield Bu/Ac 49 52 50 55 51 52 1/ 57 52 43 46 54 1/ 47 44 53 44 52 48 51 52 1/ 52 49 48 49 52 45 54 50 44 52 53 56 50 45 50 46 41 46 51 46 52 51 48 53 46 54 47 50 48 52
Purdue - CES - 02
Master Gardener Class #2008-3 ScheduleThe third series of Master Gardener classes in 2008 will be held on Wednesdays, 9:00am - 4:00pm (two 3-hour sessions per day with an hour lunch break), from October 1 - December 10, 2008. The 18-session program
Purdue - CES - 02
Master Gardener Class #2008-4 ScheduleThe fourth series of Master Gardener classes in 2008 will be held on Mondays and Wednesdays, 6:009:00pm, from October 1 December 10, 2008. The 18-session program will be held twice a week for three hours (excep
Purdue - CES - 01
Purdue Extension Marion County 6640 Intech Blvd, Suite 120 Indianapolis, IN 46278 317-275-9305Marion County Master Gardener Program (2008)Issue:Home gardening is more popular than ever. Eighty-three percent of all U.S. households (2005) partici
Purdue - ID - 220
ID-220INDIVIDUAL RESIDENCEWASTEWATER WETLANDCONSTRUCTION IN INDIANAThis is a joint publication of Purdue University and the Indiana State Department of Health as part of the on-site wastewater disposal project. It is intended for use by home
Purdue - STAT - 517
Errata and Minor ChangesAll errata have been corrected in the second printing except those preceded by (*)Chapter 1 o Challenge 1.5.15 - just before (a) change &quot;roll&quot; to &quot;rolls&quot;. o (*) Problem 1.64. - the sample space $S$ should contain the int
Purdue - CES - 05
TheJunior Master Gardener program is a way to:&gt; TEACH gardening, ecology and nutrition through experiential learning &gt; FOSTER the growth of leadership skills in youth and increase parental involvement in your community &gt; BUILD a sense of pride an
Purdue - CES - 05
Purdue - CES - 05
NATIONAL FFA NURSERY/LANDSCAPE CAREER DEVELOPMENT EVENT Description of Duties for Event Judges and AssistantsAlan R. McDaniel, Superintendent Department of Horticulture, Virginia TechFirst Day Events two cycles of half the teams in each area belo
Purdue - CES - 07
Marion County Master Gardener Association Membership FormThe Marion County Master Gardener Association is a nonprofit organization whose purpose is to promote good gardening practices in cooperation with Purdue Extension-Marion County. Members of th
Purdue - CES - 07
Indiana Master Gardener Photo Contest - 2008A statewide photo contest for Indiana Master Gardeners will be part of the 2008 Indiana Master Gardener State Conference, which is being hosted in Indianapolis by the Marion County Master Gardener Associat
Purdue - CES - 07
The conference officially begins at 1:00 p.m. on Friday. But come early and partake in -Crime Scene Investigators!Come Join Peggy Sellers, Master Gardener State Coordinator, as she delves into the world of plant problem diagnostics through the eye
Purdue - CES - 07
Youre invited to a specialEvening Meeting of the Marion County Master Gardener AssociationWednesday, September 27th, 2006 5:30 to 8:15 PMIndiana State Museum 650 West Washington Street5:30 to 7:00 PMOpen House TimeRefreshments and socializi
Purdue - CES - 07
Purdue Universitys 2007 Master Gardener State ConferenceSeptember 27, 28, and 29 Aztar Hotel and Executive Conference Center Evansville, IndianaEverything Under One Roof!Hosted by Southwestern Indiana Master Gardener Association, Inc. SWIMGA Ser
Purdue - CES - 07
Marion County Master Gardener Association MeetingJanuary 12, 2009 9:30-11:30 AMPurdue Extension Marion County Office 6640 Intech Blvd. Indianapolis, IN 46278Join Steve Mayer, Mayer Extension Educator-Horticulture, For a presentation onWhats Ne