Questions with Complete Solutions - Hamro CSIT

Factorize the matrix using Cholesky’s decomposition.

\(\begin{bmatrix}1 & 2 & 3\\ 2 & 8 & 22\\ 3 & 22 & 82\end{bmatrix}\).

Not Answered Numerical Method

Calculate the integral value of the following tabulated function from x = 0 to x = 1.6 using simpson’s 3/8 rule.

x 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

f(x) 0 0.24 0.55 0.92 1.63 1.84 2.37 2.95 3.56

Not Answered Numerical Method

Find the largest eigen value and the corresponding eigen vector of the following matrix :

\(\begin{bmatrix}1 & 2 & 0\\ 2 & 1 & 0\\ 0 & 0 & -1\end{bmatrix}\).

Not Answered Numerical Method

Using a method of least square find the relation of the form y = ax+b

x 0.301 0.4771 0.6021 0.6990

y 1.4440 1.7931 2.0414 2.2068

Not Answered Numerical Method

Use Romberg estimate to evaluate R(2,2)

$$∫\frac{{1}}{{1+x}} $$ from 0 to 2.

Not Answered Numerical Method

What do you mean by ill condition? Compare Gauss elimination method and Gauss jordan method of solving simultaneous equations.

Using Gauss jordan method solve the given system of equation

6x₁ – 2x₂ + x₃ = 11

x₁ + 2x₂ – 5x₃ = -1

-2x₁ + 7x₂ + 2x₃ = 5

Not Answered Numerical Method

Define the terms interpolation and extrapolation. Find the Langrange interpolation polynomial to fit the following data and find value of y(10).

x 5 6 9 11

y 12 13 14 16

Not Answered Numerical Method

Solve the ordinary differential equation given below by using Eular,s method. And calculate the value of y’ = 3x²+ 1 ; y(0) = 2, when

h = 0.5

h = 0.25

Not Answered Numerical Method

Find the missing term in the following using Newton’s divided difference formula.

x 0 1 2 3 4

y 1 3 9 …. 81

Not Answered Numerical Method

Give the brief concept of Flynn’s classification.

Not Answered Computer Architecture

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