Product Number TCG037
THE CRIMSON PRESS CURRICULUM CENTER
THE CRIMSON GROUP, INC.
Narcolarm, Inc. (A)
Not long after completing her residency in neurology, Mary Lou Black, M.D., became quite
dise
Math 6800: Solutions for Problem Set 5
W.D. Henshaw
1. Let A, B Cmm be nonsingular and let (A) be the condition number of A. Let
any induced matrix norm.
denote
(a) Show that for any induced norm wher
W.D. Henshaw
Math 6800: Solutions for Problem Set 6
1. NLA 19.1 Given A Cmn of rank n and b C, .
Solution:
Written out the equations are
r + Ax = b,
A r = 0.
Multiplying the rst equation by A and usin
Homework 4
1. Consider V a vector space of all degree three polynomials defined on [1, 1]. Given basis
(1, x, x2 , x3 ), we will find an orthonormal basis of V using Gram-Schmidt. Let a1 = 1, a2 =
x,
Homework 3
6.1 Let P be an orthogonal projector. Then, P 2 = P and P = P . So P P = P and we have:
(I 2P )(I 2P ) = (I 2P )(I 2P ) = I 2P 2P + 4P P = I 2P 2P + 4P = I
Thus, I 2P is unitary. Geometrica
Homework 6
1. First we show that every induced norm is sub-multiplicative by first showing kA~xk kAkk~xk.
Assume, BWOC, kA~xk > kAkk~xk. Then, k~x1k kA~xk > kAk = kA k~xxk k > kAk. This is a
contradic
Homework 5
1. (Eigenvalues) Consider the eigenvalue with corresponding eigenvector ~x 6= ~0 of F , then
F ~x = ~x. Also we know F 2 = I, so we have
~x = I~x = F 2 ~x F ~x = F 2 ~x ~x = F ~x ~x = 2 ~x
Introduction:
Financial and Mathematical Modeling
Professor Chanaka Edirisinghe
Lally School of Management
Rensselaer Polytechnic Institute
Edirisinghe, MGMT-6520
1
Why invest?
Retirement? College tu
Financial Computation
Fall 2016
HW # 3: Solving Nonlinear Equations
Please submit all .m files onto LMS.
Please submit four .m files:
1. myHW3.m (which is a master script that answers all four questio
Financial Computation
Fall 2016
HW # 2: Introduction to Numerical Methods
Please submit all .m files via LMS. Due at the start of class 9/15 or 9/16.
1. Write a function in MATLAB to convert a decimal
Financial Computation
Fall 2016
HW # 1: Introduction to MATLAB
Please submit all .m files via email via LMS. Due at the start of Lecture 2 (9/8 for section 01 and 9/9
for section 02).
The Black-Schole
Homework 1
1.
0
1
a) Given basis B1 = cfw_1, x, x2 , x3 , we have L1 =
0
0
d
tion for dx : V V . We can see this because
0
0
2
0
0
0
0
3
0
0
as the matrix representa0
0
d
(a0 , a1 , a2 , a3 ) = (a1
Homework 2
4.1
c) We have,
0 0
1 0 0 0 1 0
A A=
=
0 4
0 1 0 4 0 1
T
Now, we see that the diagonal entries of our middle matrix are
now write it as:
v
u
u 4 0
2
u
0 1 4 0 0 1
T
A A=
then we have =
Math 6800: Solutions for Problem Set 4
W.D. Henshaw
1. Consider the Householder reector,
F = I 2uu ,
u u = 1.
Determine the eigenvalues and eigenvectors, determinant, and singular values of F .
Soluti
W.D. Henshaw
Math 6800: Solutions for Problem Set 7
1. A matrix D is block tridiagonal if it is of the form
B1 C1
A2 B 2 C 2
A3 B 3 C 3
D=
A4 B4
.
.
C4
.
.
.
.
An Bn
where each Ai , Bi and Ci is a sm
Computational Linear Algebra
Math 6800, Fall 2015
Instructor: W.D. Henshaw ([email protected]), Oce: Amos Eaton 304
Lectures: Monday and Thursday, 1011:50am, Carnegie 208.
Class web page: See link from w
Math 6800: Midterm Exam Solutions
W.D. Henshaw
Name:
Instructions:
Time for the exam is 1hour, 50 minutes.
Please answer all 5 problems.
The weights for the problems are approximately equal.
Answe
Math 6800
D. Schwendeman
1. Text exercise 3.1.
2. Text exercise 3.5.
3. Text exercise 4.1(a,c,e only).
4. Text exercise 4.4.
5. Text exercise 5.3.
6. Text exercise 6.1.
7. Text exercise 6.4.
Problem S
Math 6800: Solutions for Problem Set 3
W.D. Henshaw
1. NLA exercise 6.5 Let P Cmm be a nonzero projector. Show that P
and only if P is an orthogonal projector.
2
1, with equality if
Solution:
Solutio
Math 6800: Solutions for Problem Set 1
W.D. Henshaw
1. NLA exercise 1.1 Let B be. Solution:
Let Ak denote the operation in step k, so that
A5 A3 A2 BA1 A4 A6 A7
and
1 1
0 1
0 1
0 1
0 0 1
0 0 0
1 0 0
0
Complex Variables Cheat Sheet
A complex number is written as z = x + iy where x and y are real numbers and i2 = 1. We
write (z) = x (or Re(z) for the real part of z and (z) = y (or Im(z) for the imagi
Financial Computation
Fall 2016
HW # 4: Optimization (1)
Please submit all .m files onto LMS by the start of class on 9/29 or 9/30.
Please submit the following .m files:
1.
2.
3.
4.
myHW4.m
mySteepest
w
wi
w
n+1
w(x)
w
1
x0
x1
x
i-1
xi
x
i+1
xn+1
x
y, j
N
(i,j)
j
1
j=0
i=0
1
i
N
x, i
(0,3)
(1,3)
(2,3)
(3,3)
(0,2)
(1,2)
(2,2)
(3,2)
(0,1)
(1,1)
(2,1)
(3,1)
(0,0)
(1,0)
(2,0)
(3,0)
X
X
X
XX
X
X
X
X
X
X
Math 6800
D. Schwendeman
Problem Set 7
Due:
Monday, 11/22/10
1. Text exercise 27.5, p.210.
2. Text exercise 28.1, p.218.
3. Text exercise 28.2, p.218.
4. Construct an algorithm that computes the QR-fa
Math 6800
D. Schwendeman
Problem Set 6
Due:
Monday, 11/8/10
1. Text exercise 23.2, p.177.
2. Consider the linear system Ax = b, where A is a symmetric, positive denite matrix.
(a) Write a matlab funct
Math 6800
D. Schwendeman
Problem Set 5
Due:
Thursday, 10/28/10
1. Text exercise 20.2, p.154. (What are the bandwidths of the factors L and U of A? What
is the maximum number of nonzero elements in any
Math 6800
D. Schwendeman
Problem Set 4
Due:
Tuesday, 10/12/10
1. Text exercise 10.4, p.76.
2. Let f (x) = 1/(1 x2 ). Find (f ) for an innitesimal perturbation about x. For
what values of x is f ill-co
Math 6800
D. Schwendeman
Due:
Thursday, 9/30/10
Problem Set 3
1. (a) Write a computer subroutine (or Matlab function) that computes the reduced QRfactorization of an m n real matrix A using the modied