Chapter Two Numerical Solution of Systems of Linear
Equations
(MA5625)
In this chapter, we consider the linear system
Ax = b .
where A = (aij )n =1 is an n n matrix and b is an n-dimensional vector. We always assume
i,j
that A is nonsingular, i.e., det(A)
Lecture Notes
for Numerical Methods (MA5625)
Weiwei Sun
Chapter One Numerical Solution of Nonlinear
Equations
1.1 Introduction
This chapter is devoted to the problem of locating roots of equations(or zeros of functions). The problem occurs frequently in s
Assignment 1 (MA5625)
Q1. Give a formula involving a0 , b0 , and for the number of steps that should be taken
in the bisection algorithm to ensure that the root is determined with relative precision .
Assume a0 > 0.
Q2. Write and test a subprogram to impl
Assignment #3 (MA5625)
Q1. Let
0.8
0.3
x=
Calculate x
l
0.9
0.3
x=
1 1 0
3
5
0
0 3 1
and A l , l = 1, 2, , respectively.
Q2. Let x be an m-vector and A be an n m matrix. Show that
(i) 1m x x 2 m x ,
(ii) 1m A A 2 n A .
Q3. Let A be a square matrix. P