2072U
Tutorial week 4, 2014
Error analysis
Construct a matrix V with the following elements:
Vij =
(1)i+j
, i, j = 1, . . . , N
i + 2j
and let r be the rst column vector of V .
For N = 2, . . . , 10,
2072U
ASSIGNMENT 1, 2014
Iteration and recursion
Due: Friday, January 24th, 8:10. Hand in your assignment in at the lecture.
Write your answers out carefully and clearly. Upload the following Matlab
l
2072U
ASSIGNMENT 2, 2014
Linear systems and complexity
Due: Friday, February 7, 8:10. Hand in your assignment in at the lecture.
Write your answers out carefully and clearly. Upload the following Matl
MATH 2072U
Midterm Examination solutions
Instructor: L. van Veen
February 27, 2014
1. Consider the nonlinear equation
exp( x ) x exp( x ) = 0
This equation has a solution x [0, 1].
(a) [10 marks] Find
MATH 2072U
Midterm Examination
Instructor: L. van Veen
March 2nd, 2017
9:40-11:00
1. Consider the nonlinear equation
2( x + 1) sin( x ) 1 = 0
This equation has a unique solution x [1, 1].
(a) [10 mark
2072U Computational Science I
winter 2012
Week
1
12
34
5
6
78
910
11
12
13
Topic
Introduction
Solving nonlinear equations in one variable
Solving systems of linear equations
Computational complexity
R
2072U
Tutorial week 7, 2014
Products of polynomials
In Matlab, polynomials are represented by vectors. The elements of the vector are the polynomial
coecients, listed in decreasing order see the help
2072U
Tutorial week 6, 2014
The Vandermonde matrix
Suppose we want to nd a polynomial
Pn = a0 + a1 x + . . . + an xn
that ts the data points (xi , yi ) for i = 0, . . . , n.
For n = 3, write out the
2072U
ASSIGNMENT 3, 2014
Interpolation and more pseudocode
Due: Friday, February 28, 8:10. Hand in your assignment in at the lecture.
Write your answers out carefully and clearly. Upload the following
2072U
Tutorial 1, 2014
Iteration and bisection
In the rst lecture we saw the iterative method
x(k+1) = (x(k) ) =
a
1 (k )
x + (k)
2
x
We also saw that, starting from x(0) = 3 with a = 5, after ve iter
2072U
Tutorial week 3, 2014
On computing the determinant. . .
In this tutorial you will compare two methods for computing the determinant of a matrix. You
have probably learned what the determinant is
2072U
Tutorial week 5, 2014
Flop counting
Exercise A
Consider a banded matrix:
A GL(n, n) with Aij = 0 for j > i + b or i > j + b
We say that A has band width b. On each row it has at most 2b + 1 nonz
2072U Computational Science I
winter 2014
Week
1
12
34
5
6
78
910
11
12
13
Topic
Introduction
Solving nonlinear equations in one variable
Solving systems of linear equations
Computational complexity
R
2072U Computational Science I
winter 2012
Week
1
12
34
5
6
78
910
11
12
13
Topic
Introduction
Solving nonlinear equations in one variable
Solving systems of linear equations
Computational complexity
R
2072U Computational Science I
winter 2013
Week
1
12
34
5
6
78
910
11
12
13
Topic
Introduction
Solving nonlinear equations in one variable
Solving systems of linear equations
Computational complexity
R
2072U Computational Science I
winter 2014
Week
1
12
34
5
6
78
910
11
12
13
Topic
Introduction
Solving nonlinear equations in one variable
Solving systems of linear equations
Computational complexity
R