1
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Handout 7, 27 March 2012
Some useful relationships about vector and matrix norms.
The fundamental principle: A vector or matrix norm is a real scalar, used to measure the size of vectors
1
Numerical Computing
New York University, Spring 2012
Margaret Wright
Handout 3, 31 January 2012
Using the secant method to nd a zero of f (x) = 1.2 0.9x4 with
x0 = 0.4 and x1 = 1.2.
2
1.5
1
0.5
x1
0
x0
x2
0.5
1
1.5
2
2.5
3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.
NUMERICAL COMPUTING
V22.0421-001
New York University
Spring Semester 2012
Instructor: Margaret H. Wright
January 26, 2012
Handout 1Class meeting 2
1.
Order notation
The following notation is ubiquitous in analyzing many algorithms in numerical computing.
1
Numerical Computing
New York University, Spring 2012
Handout 5, 20 March 2012
Untidy calculations in the linear least-squares problem.
Let A be an m n matrix, m n, whose columns are linearly independent (so that A has full column rank),
and suppose that
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Instructor: Margaret H. Wright
Homework Assignment 8
Assigned April 12, 2012; due April 19, 2012
Exercise 7.1. Assume that we wish to interpolate the function f (x) in the interval [a, b]
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Instructor: Margaret H. Wright
Homework Assignment 7
Assigned April 3, 2012; due April 10, 2012
Exercise 7.1. Dene A and b as
6
3
A = 4 1.99999 ,
2
1
6
b = 6 .
2
(a) Give the singular valu
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Instructor: Margaret H. Wright
Homework Assignment 6
Assigned March 22, 2012; due March 29, 2012
Exercise 6.1. This problem involves the (silly) model discussed in class, based on the theo
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Instructor: Margaret H. Wright
Homework Assignment 5
Assigned March 1, 2012; due March 8, 2012
Exercise 5.1. Let b denote a given n-vector, let e denote the n-vector whose components are a
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Instructor: Margaret H. Wright
Homework Assignment 4
Assigned February 21, 2012; due March 1, 2012
In all problems involving vector or matrix norms, assume that the two-norm is used unless
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Instructor: Margaret H. Wright
Homework Assignment 3
Assigned February 14, 2012; due February 21, 2012
Exercise 3.1.
Given a real nonzero number x, by convention the value y = x0 (x raised
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Instructor: Margaret H. Wright
Homework Assignment 2
Assigned February 7, 2012; due February 14, 2012
Exercise 2.1. (Special conditions for Newtons method.) Consider using Newtons method
t
CSCI-UA.0421: Numerical Computing
New York University, Spring 2012
Instructor: Margaret H. Wright
Homework Assignment 1
Assigned January 31, 2012; due February 7, 2012
Exercise 1.1. (Sequences and rates of convergence.)
k
(a) Compute and print the rst 11
1
Numerical Computing
New York University, Spring 2012
Margaret Wright
Handout 4, 9 February 2012
Hexadecimal digits
decimal
8
9
10
11
12
13
14
15
symbol
8
9
a
b
c
d
e
f
bit pattern
1000
1001
1010
1011
1100
1101
1110
1111
11-bit exponent bitstrings in IEE
1
Numerical Computing
New York University, Spring 2012
Margaret Wright
Handout 2, 26 January 2012
Using bisection to nd a zero of f (x) = x2 9, with initial interval
[0, 10], so that f (a) = 9 and f (b) = 91.
f (ak )
f (bk )
9
9
2.75
2.75
2.75
1.0898
1.86