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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

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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

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Refer to Intro to PDEs notes.
1. Classification of PDEs
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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
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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

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Lecture 3
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cmda 3606; mark embree
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The singular value decomposition (SVD) is among the most
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natural way to untangle a matrix into its four f

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Numerical Analysis: Linear Algebra
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Solutions to Homework 4
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Date Due: Oct 1, 2008
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Householder reflector F = I 2 vvv

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For any x1 , y1 , x2 , y2 , x, y Cm , , C,
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x (y1 + y2 ) = x y1 + x y2 ,
(x) (y) =
x y.
(That is, the inner product is bilinear ).
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1 If u and v are m-vectors, the matrix A = I + uv is known as a rank-one perturbation of the identity. Show
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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: