Quantitative Methods Answers

Give the most compact theta notation for the number of times the statement
x = x + 1 is executed in the following pseudo-code:
for i = 1 to i = 3n − 1{
for j = 1 to j = n{
x = x + 1
}
}

Let f(n) and g(n) be functions with domain {1, 2, 3, . . .}. Prove the following:
If f(n) = Ω(g(n)), then g(n) = O(f(n)).

b) Set up the Gaussi-Jacobi iteration scheme in matrix form for the linear system of equations

4 3
4 2
4 3
2 3
1 2 3
1 2
− + =
− + − =
− =
x x
x x x
x x

Show that the iteration scheme is convergent. Hence find the rate of convergence of this
method.

2. a) Find by Newton’s method the roots of the following equations correct to three places of
decimals.
i) log .4 772393 x 10 x = near x = 6 .
ii) f (x) = x − 2sin x near x = 2 .

b) Solve the IVP, ; )4(y 4
x 4y
1
y
2
=
−
′ = using Euler’s method. Find )2.4(y with h = 2.0
and 1.0 and extrapolate the value )

c) Obtain the cube root of 12 using Newton-Raphson formula.

Draw a flowchart that reads the names , sex and score of each student and outputs the names of the male students that scored above 75% and how many they are?

use newton's method to approximate SQRT of 11 to 5 decimal places

The technique of determining an approximate value of f(x) for a non-tabular value of x which lies outside the internal [a, b] is known as............

For the given functions f (x), let x0 = 0, x1 = 0.6, and x2 = 0.9. Construct interpolation polynomials
of degree at most one and at most two to approximate f (0.45), and find the absolute error.
a. f (x) = cos x