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 |
To estimate the population in 1985 using numerical analysis, we can apply the method of interpolation, since the year 1985 lies between 1981 and 1991. The data points closest to 1985 are (1981, 15) and (1991, 20). Linear interpolation is a suitable approach for ____ __________ _________ _____ _______ ____ _______ ____.
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Using synthetic division method, check whether α = 3 is a root of the polynomial equation:
x4 + x3 - 13x2 - x + 12 = 0
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 |
Given the data:
f(3) = 168,
f(7) = 120
and f(9) = 72
If f(k) is estimated as 138 using the Newton’s form of the interpolating polynomial, then find the value of .k
Find the inverse of the matrix:
using LU decomposition method with u11 = u22 = u33 = 1.
Calculate the nth divided difference of 1/x, on the nodal points X0 , X1 , ......., Xn .
Using Newton-Rapshson method, find an iterative formula to compute the reciprocal of a natural number N.
Using the data sin (0.1) = 0.09983 and sin (0.2) = 0.19867, find an approximate value of sin (0.15) by Lagrange’s interpolation. Also obtain a bound on the truncation error.