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Quantitative Methods
Compute the largest eigenvalue in magnitude, and the corresponding eigenvector of
the matrix
A=1 −1 1
2 0 3
1 4 −1
by performing four iterations of the power method
the matrix
A=1 −1 1
2 0 3
1 4 −1
by performing four iterations of the power method
Quantitative Methods
Compute integral 0 to 4 f(x)dx using the Romberg integral technique on the trapezoidal integrals evaluated by the trapezoidal rule taking h = 1 and h = 0.5. The tabulated
values are given below.
x 0 0.5 1 1.5 2.0 2.5 3.0 3.5 4.0
f(x) 1 4 3 2 2.5 2.9 3.6 4 1.8
values are given below.
x 0 0.5 1 1.5 2.0 2.5 3.0 3.5 4.0
f(x) 1 4 3 2 2.5 2.9 3.6 4 1.8
Quantitative Methods
Use Euler’s method to solve the I.V.P.
y'=(x-y)/2, on [0,3], with y(0) = 1, and h = 0.5
y'=(x-y)/2, on [0,3], with y(0) = 1, and h = 0.5
Quantitative Methods
Find a root of the equation 3x^3+10x^2+10x+7 = 0 which is close to −2.0, using
the Berge -Vieta method. Perform two iterations of the method.
the Berge -Vieta method. Perform two iterations of the method.
Quantitative Methods
Determine the maximum error in quadratic interpolation at equispaced points.
Quantitative Methods
Taking the endpoints of the last interval obtained in part a) above as the initial
approximations, perform two iterations of the secant method to approximate the
root.
approximations, perform two iterations of the secant method to approximate the
root.
Quantitative Methods
Find the interval of unit length that contains the smallest positive root of the
equation f(x) = x^3 −5x^2+1 = 0. Starting with this interval, find an interval of
length 0.05 or less that contains the root, by Bisection method.
equation f(x) = x^3 −5x^2+1 = 0. Starting with this interval, find an interval of
length 0.05 or less that contains the root, by Bisection method.
Quantitative Methods
Find the inverse of the matrix
1 −1 4
2 9 8
6 5 2
using LU decomposition method.
1 −1 4
2 9 8
6 5 2
using LU decomposition method.
Quantitative Methods
Compute the largest eigenvalue in magnitude, and the corresponding eigenvector of the matrix
A =1 −1 1
2 0 3
1 4 −1
by performing four iterations of the power method.
A =1 −1 1
2 0 3
1 4 −1
by performing four iterations of the power method.
Quantitative Methods
Find the inverse of the following matrix, using Gauss Jordan method.
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
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