QUIZ2
practice LastName_FirstName_
1. Understand Figure 3.6 Page 103 from the book.
(
)
2. A sufficient condition to prove convergence of an iterative method
is to show that the error at the
step is less than the error at
step, i.e.

 

in some inter
HW3
1. Write Matlab program that implements the fixed point iteration method x(k+1)=g(xk) k=1,2,
with a stopping criterion, the xkx(k1)<tol, and a max number of iterations kmax. Then solve the
equation f(x)=x23x+2 by using the following iteration fu
HW2
1. Taylors polynomial approximating a function is defined as follows
() = () +
=1
() =
() ()( )
!
+1
( )
() (),
, .
( + 1)!
() = () + ().
The tangent line at the point 0 is the first degree Taylors polynomial 1 () = (0 ) +
(0 )( 0 ) that has as
HW5
1.
Another form of the error for Trapezoidal rule can be given by The General Euler
McLaurin formula is defined by ,
() = ( ) + 1 () + ()
=0
=1
2 2 (21)
() (21) () +
(
(2)!
Where the Bernoulli numbers are given by
1
1
1
1
1
1 = 2 , 2 = 6 , 3 = 0,
HW1
1. Taylors polynomial approximating a function is defined as follows
() = () +
=1
() =
() ()( )
!
+1
( )
() (),
, .
( + 1)!
() = () + ().
Matlab can implement the above approximation using a combination of symbolic computation
and classical pro
HW4
1. The following data are taken from a polynomial () of degree 5. What is the polynomial and what
is its degree.[Use Newtons method]
x
2
1
0
1
2
3
p(x)
1
1
7
25
5
1
2. Matlab has built in functions for computing and evaluating interpolation C=poly
QUIZ1 LastName_FirstName_
1. Taylors polynomial approximating a function is defined as follows
( )
( )
( )
(
)
(
)
( )
( )
( )
( )(
)
( )
( )
( )
i.
Find the Taylors polynomial and error for ( )
( )
ii.
Find an upper bound for the error. Show that the er
EXAM2
1.
2
Given the matrix A = [1
1
1
2
1
1
1]
2
a. What is 1 and  = 4
b. Find the inverse 1 using Gauss Jordan method.
0.7500 0.2500 0.2500
0.2500 0.7500 0.2500
0.2500 0.2500 0.7500
c. Find the condition number (, 1) and (, ) =5?
The (, ) =  1  .