Numerical Computation Questions

NUMERICAL COMPUTATION1.
Give the formula for the midpoint and Trapezoidal rules used to evaluate definite integrals
and explain the terms used.
(4 Marks)
2. a) Use Gaussian elimination technique to solve the following system of equations
=3
=2
=5
(10 Marks)
b−a

x
=
b) Given
, show the formula for approximating the integral  f ( x )dx for n
n
a
b
partitions using the trapezoidal rule.
(4 Marks)

c) Approximate the integral
 sin (x)dx using trapezoidal rule for n = 8 .
0
(8 Marks)
3) a) Consider the set of equations:
x1 + x2 = 4
x1 − 2×2 = 1
Use eight rounds of the Gauss-Seidel Iteration to solve for x1 and x2
(8 Marks)
2. Find the LU decomposition of the matrix
 25 5 1
A =  64 8 1
144 12 1
(10 Marks)
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