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Numerical analysis i questions.

Numerical analysis i questions.

Find Numerical analysis i university examination questions in acaproso.com

# Question
1

Solve the equation f(x)={x^3}-x-1=0, using the secant iteration method starting from x_{0}=1, x_{1}=2.


Mathematical Calculation
2

Use the Lagrange interpolating polynomial to show that the three point forward dufference formula for approximatingf^{`}(x_{i-1}) is given byf^{`}(x_{i-1})approxfrac{(-y_{i+1}+4y_i-3y_{i-1})}{x_{i+1}-x_{i-1}}

assume that the three data points are evenly spaced.


Mathematical Calculation
3

Find the positive root of tan(pi x)-6=0 in [0,0.48] using the method of falsi position five iterations.


Mathematical Calculation
4

Find the root of the equation x^3-x^2=1, using iteration method (do 4 iteration)


Mathematical Calculation
5

Using Newton`s method to find a positive real root of cos(x)-x^3=0 (do 5 iteration)


Mathematical Calculation
6

Find the positive root off(x)=x^3-6x^2+11x-6=0 using bisection method (do 4 iteration)


Mathematical Calculation
7

Establish a linear interpolating polynomial and computeln(9.2) from ln9.0 = 2.1972, ln9.5 = 2.2513 by newton`s interpolating polynomial and determine the error from ln9.2 = 2.2192


Mathematical Calculation
8

Approximate the positive square root 2 using Newton`s method with x_0=1.5 (do 4 iteration)


Mathematical Calculation
9

Given the general points {(x_1,y_1),(x_2,y_2), ..........,(x_n,y_n)}

  • derive the general form of the Lagrange Polynomials so thaty_1=f(x_1) for i = 1, n.
  • from (A) above, show that Lagrange Polynomial can be expressed as linear combination  of L_k
  • write the Langrange polynomial for the data below and interpolate the value of y given x = 0.5
x -1 0 1
y 1 -1 2

 


Mathematical Calculation
10

What is the two`s complement  of the binary number 10010010?


Mathematical Calculation