Math 514 F15, Homework Assignment 5 - FD Methods for the Heat Equation
Due Friday, Dec. 4.
The homework can be submitted either in class or by e-mail by 11:59pm on the due date. Your
work must be combined into a single pdf file.
In this homework we will c
Math 514 F15, Homework Assignment 4 - Implicit Methods for ODE
Due Tuesday, Nov. 17.
The homework can be submitted either in class or by e-mail by 11:59pm on the due date. Your
work must be combined into a single pdf file. Do not forget to submit a copy o
Math 514 F15, Exam 2 Review
Partial Differential Equations (PDEs)
Refer to Intro to PDEs notes.
1. Classification of PDEs
2. Be able to check that a given function is a solution to a given PDE.
Solving time dependent PDEs using Finite Differences.
We have
Math 514 F15, Homework Assignment 5 - FD Methods for the Heat Equation
Due Friday, Dec. 4.
The homework can be submitted either in class or by e-mail by 11:59pm on the due date. Your
work must be combined into a single pdf file.
In this homework we will c
Analysis I
Piotr Hajlasz
1
Measure theory
1.1
-algebra.
Definition. Let X be a set. A collection M of subsets of X is -algebra if M has the
following properties
1. X M;
2. A M = X \ A M;
3. A1 , A2 , A3 , . . . M =
S
i=1
Ai M.
The pair (X, M) is called me
Introduction to Statistics
1
Lecture 3
Outliers
An outlier is a data value that does not follow
the pattern of the other observations. Usually it
is too large or too small, compared with the other
values.
An outlier can occur because of an error in
measur
CS 61002 Lab#1
Spring 2016
(1) Working Copy Setup
The checkout commands done below put the checked out directories in your home directory. Put
the checked out directories in another directory if you prefer.
The directories cs61002 and shared should be in
RS Chapter 2 Random Variables
8/19/2015
Chapter 2
Random Variables
Random Variables
A random variable is a convenient way to express the elements
of as numbers rather than abstract elements of sets.
Definition: Let AX; AY be nonempty families of subsets
Introduction to statistics
1
Lecture II
Organizing Data
A Pareto chart is a bar graph whose bars are
drawn in decreasing order of frequency or relative
frequency.
Definition 1. A side-by-side bar graph is
used when we want to compare two sets of data.
Car
8. the singular value decomposition
cmda 3606; mark embree
version of 5 May 2014
The singular value decomposition (SVD) is among the most
important and widely applicable matrix factorizations. It provides a
natural way to untangle a matrix into its four f
CS 383C
CAM 383C/M 383E
Numerical Analysis: Linear Algebra
Fall 2008
Solutions to Homework 4
Lecturer: Inderjit Dhillon
Keywords: Householder Triangularization, Least Squares Problem
Date Due: Oct 1, 2008
1. Problem 10.1
Householder reflector F = I 2 vvv
Lecture 4. The Singular Value
Decomposition
The singular value decomposition (SVD) is a matrix factorization whose computation is a step in many algorithms. Equally important is the use of the
SVD for conceptual purposes. Many problems of linear algebra c
Tests and p-values
Suppose you have observations x1 , x2 , . . . , xn that come from some real world
process. You can interpret this as follows: x1 , x2 , . . . , xn are part of an infinite
sequence x1 , x2 , . . . , which is an instance of a sequence X1
Orthogonal vectors and unitary matrices
Inner product
For any x1 , y1 , x2 , y2 , x, y Cm , , C,
(x1 + x2 ) y = x1 y + x2 y,
x (y1 + y2 ) = x y1 + x y2 ,
(x) (y) =
x y.
(That is, the inner product is bilinear ).
More on adjoints
For any A Cm` , B C`n
(A
RS Chapter 1 Random Variables
Chapter 1
Probability Theory:
Introduction
Definitions Algebra
Definitions: Semiring
A collection of sets F is called a semiring if it satisfies:
F.
If A, B F, then A B F.
If A, B F, then there exists a collection of sets
Brad Nelson
Math 126
Homework #1
1/16/12
1 If u and v are m-vectors, the matrix A = I + uv is known as a rank-one perturbation of the identity. Show
that if A is non-singular, then its inverse has the form A1 = I + uv for some scalar , and give an
express
Typos in Probability: Theory and Examples, 4th Edition
Contributions from Nate Eldredge, J.C. Li, Carl Mueller, Sebastien Roch, Byron Schmuland,
Antonio Sodre
Page numbers are those of the printed book.
Chapter 1
Page 2, proof of (ii) in Theorem 1.1.1. Tw
18.409 The Behavior of Algorithms in Practice
2/12/2
Lecture 2
Lecturer: Dan Spielman
Scribe: Steve Weis
Linear Algebra Review
A n x n matrix has n singular values. For a matrix A, the largest singular value is denoted
as n (A). Similarly, the smallest is
Chapter 2
Measure Spaces
2.1
Families of Sets
Definition 7 ( systems) A family of subsets F of is a system if,
Ak F for k = 1, 2 implies A1 A2 F.
A system is closed under finitely many intersections but not necessarily
under unions. The simplest example o
Stochastic calculus for summable processes
1
Lecture I
Definition 1. Statistics is the science of
collecting, organizing, summarizing and analyzing
the information in order to draw conclusions.
It is a process consisting of 3 parts.
January 19, 2016
Stoch
Chapter 1
Elements of Probability Distribution
Theory
1.1 Introductory Definitions
Statistics gives us methods to make inference about a population based on a random sample representing this population. For example, in clinical trials a new
drug is applie
SVD computation example
T
Example: Find the SVD of A, U V , where A =
3 2 2
2 3 2
.
First we compute the singular values i by finding the eigenvalues of AAT .
17 8
T
AA =
.
8 17
T
The characteristic polynomial
= 2 34 + 225 = ( 25)( 9), so
is det(AA I)
the
2
Homework Solutions
18.335 - Fall 2004
2.1
Count the number of oating point operations required to compute
the QR decomposition of an m-by-n matrix using (a) Householder
reectors (b) Givens rotations.
2 3
n ops.
3
2mn2
(a) See Trefethen p. 74-75. Answer: