CPSC 302 Assignment 1 Solution
January 28, 2011
1. Using the formula given in the question,
(a) By the denition of the derivative we straightforwardly have that
cos(x + ) cos(x)
= sin x.
h
lim
To show
CPSC 302 Assignment 1 Solution
Uri Ascher & Chen Greif
January 2014
Question 1
(a) Taylor series expansions for h give
f (x0 + h) =
f (x0 h) =
h2
f (x0 ) +
2
h2
f (x0 ) hf (x0 ) + f (x0 )
2
f (x0 )
CPSC 302 Assignment 4 Solution
March 3, 2011
Question 1
(AT A)T = AT (AT )T , so it is clearly symmetric.
xT AT Ax = (Ax)T Ax = Ax2 0.
2
(1)
Since A has full rank, Ax = 0 if x = 0, hence
xT AT Ax > 0,
CPSC 302, Winter Term, 2014
Assignment 1, due Wednesday, January 22
Please show all your work: provide a hardcopy of the entire assignment (including
plots and programs); in addition, e-mail your Matl
CPSC 302, Winter Term, 2014
Assignment 2, due Wednesday, February 5
Please show all your work: provide a hardcopy of the entire assignment (including
plots and programs); in addition, e-mail your Matl
CPSC 302 Assignment 4 Solution
April 4, 2011
Question 1
(a) If A is symmetric positive denite, then we have a Cholesky decomposition
A = LLT .
Then
xA =
xT Ax =
(LT x)T (LT x) = LT x2 .
Hence the axio
CPSC 302 Assignment 2 Solution
February 11, 2011
Question 1
Let f (x) = xg(x). Then f (a) = ag(a) 0, since a g(a) b. Similarly
f (b) 0. Therefore f (a)f (b) 0 with f dened and continuous on [a, b].
Th
.
.
Chapter 2: Roundoff errors
Uri Ascher
UBC Computer Science
Department of Computer Science
University of British Columbia
[email protected]
http:/www.cs.ubc.ca/cs302/302/index.html
Uri Ascher (UBC C
Clicker Questions for L04: Numerical Algorithms &
Errors
CPSC 302: Numerical Computation for Algebraic Problems
Jessica Bosch
[email protected]
http:/www.cs.ubc.ca/~jbosch
University of British Columbi
CS 302
Term I, 2015-2016
8. Eigenvalues
Uri M. Ascher
Department of Computer Science
The University of British Columbia
[email protected]
https:/www.cs.ubc.ca/cs302/302/
Goals
Goals of this chapter
fi
Clicker Questions for L13: Review Linear Algebra
CPSC 302: Numerical Computation for Algebraic Problems
Jessica Bosch
[email protected]
http:/www.cs.ubc.ca/~jbosch
University of British Columbia
Depart
Clicker Questions for L09: Nonlinear Equations in
One Variable
CPSC 302: Numerical Computation for Algebraic Problems
Jessica Bosch
[email protected]
http:/www.cs.ubc.ca/~jbosch
University of British C
Clicker Questions for L03: Numerical algorithms &
Errors
CPSC 302: Numerical Computation for Algebraic Problems
Jessica Bosch
[email protected]
http:/www.cs.ubc.ca/~jbosch
University of British Columbi
CS 302
Term I, 2015-2016
4. Linear algebra background
Uri M. Ascher
Department of Computer Science
The University of British Columbia
[email protected]
https:/www.cs.ubc.ca/cs302/302/
Goals of this cha
Clicker Questions for L17: Direct Methods for Linear
Systems
CPSC 302: Numerical Computation for Algebraic Problems
Jessica Bosch
[email protected]
http:/www.cs.ubc.ca/~jbosch
University of British Col
CS 302
Term I, 2015-2016
6. Linear least squares
Uri M. Ascher
Department of Computer Science
The University of British Columbia
[email protected]
https:/www.cs.ubc.ca/cs302/302/
Goals of this chapter
Final Exam, CPSC 302, FALL 2011
Dec. 12, 2011
Instructions :
Write down your name and student number in the designated spot in
the booklet.
Make sure this exam has 4 pages.
1
Time: 2 2 hours.
Ther
Question 3
q = 3, a = 10
q = 2, a = 0
q = 2, a = 2
q = 3, a = 2
q = 2, a = 10
q = 3, a= 0
Note: for q = 3, a = 0, the number of iterations was too large to display all
values of x and fx along the way
Clicker Questions for L06: Numerical Algorithms &
Errors
CPSC 302: Numerical Computation for Algebraic Problems
Jessica Bosch
[email protected]
http:/www.cs.ubc.ca/~jbosch
University of British Columbi
Clicker Questions for L12: Review Linear Algebra
CPSC 302: Numerical Computation for Algebraic Problems
Jessica Bosch
[email protected]
http:/www.cs.ubc.ca/~jbosch
University of British Columbia
Depart
Clicker Questions for L15: Direct Methods for Linear
Systems
CPSC 302: Numerical Computation for Algebraic Problems
Jessica Bosch
[email protected]
http:/www.cs.ubc.ca/~jbosch
University of British Col
CPSC 302 Assignment 3 Solution
Uri Ascher & Chen Greif
February 2014
Question 1
By denition, A
1
= max
m
A
1
=
x
n
1 =1
m
n
n
aij xj max
max
x
Ax 1 . So,
1 =1
i=1
x
j=1
1 =1
|aij |xj | = max
x
i=1 j=1
CPSC 302, Winter Term, 2014
Assignment 3, due Wednesday, February 26
Please show all your work: provide a hardcopy of the entire assignment (including
plots and programs); in addition, e-mail your Mat
CPSC 302 Assignment 2 Solution
Uri Ascher & Chen Greif
February 2014
Question 1
(a) Here is our script.
x = 1.94:.001:2.08; % evaluation mesh
c = [-512,2304,-4608,5376,-4032,2016,-672,144,-18,1];
np1
CPSC 302, Winter Term, 2014
Assignment 4, due Wednesday, March 19
Please show all your work: provide a hardcopy of the entire assignment (including
plots and programs); in addition, e-mail your Matlab
CPSC 302 Assignment 4 Solution
Uri Ascher & Chen Greif
March 2014
Question 1
(a)
x = 0:.1:1;
y = [0.9,1.01,1.05,0.97,0.98,0.95,0.01,-0.1,0.02,-0.1,0.0];
plot (x,y,o)
This gives the data in blue circle