Estimate the eigen values of the matrix:
using the Gerschgorin bounds. Also, draw the rough sketch of the region in which the eigen values lie.
For estimating the eigenvalues of a matrix using Gerschgorin bounds, each eigenvalue lies within at least one of the Gerschgorin discs. Consider a square matrix $A = [a_{ij}]$ of order $n$. The Gerschgorin discs are defined _________ ________ _________ _____ ___ ________ _________ ___ _________ _________.
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If
f(x) = eax ,
show that
) Use the Euler’s method to solve numerically the initial value problem:
with h = 2.0 on the interval [0, 1].
Find one root of the equation:
x3 - 2x 5 = 0
in the interval [3,2] using Birge-Vieta method. Perform only one iteration.
Solve the system of equations:
x + 2y + z = 3
3x − 2y − z4 = −2
2x + 3y − z = −6
using Gauss-Elimination method.
From the following data, calculate the population in the year 1985:
| Year | Population (in , 000) |
| 1971 | 12 |
| 1981 | 15 |
| 1991 | 20 |
| 2001 | 27 |
| 2011 | 49 |
Calculate the nth divided difference of 1/x, on the nodal points X0 , X1 , ......., Xn .
Estimate the eigen values of the matrix:
using the Gerschgorin bounds. Also, draw the rough sketch of the region in which the eigen values lie.