By decinnial census, the population of a town was given below
Year (x) : 1971 1981 1991 2001 2011
Population (y): 112 132 158 189 226 (in thousands)
(i) Using Stirling's central difference formula, estimate the population for the year 2006
(ii) Using Newton's forward formula, estimate the population for the year 1992.
(iii) Using Newton's backward formula, estimate the population for the year 1980.
We are given population data at 10-year intervals: | Year (x) | Population (y in ___ _________ _____ _______ _____.
______ _________ ____ ___ ________ _________ ____ ______ _________.
____ _______ _______ ______ _____ ___ _________ ___ _____ ____.
________ ____ ___ ______ ____.
_____ ___ ___ _______ _______ ___ ____ ______ _________ _______.
_________ _____ ___ _________ __________.
____ __________ __________ _______ _____ __________ ______.
_________ _______ _________ _____ ___ ___ ____ ________ _________ ______.
____ _______ __________ _______ ___ ___ _________.
____ _______ ________ ___ _________ ___ _______ ___.
______.
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If values of the function
find the Lagrange's interpolation polynomial of f(x). Also, find f
For the following data develop difference table and find forward differences and backward differences
| I | xi | yi |
| 0 | -1 | 16.8575 |
| 1 | 0 | 24.0625 |
| 2 | 1 | 16.5650 |
| 3 | 2 | -13.9375 |
| 4 | 3 | 28.5625 |
| 5 | 4 | 144.0625 |
Explain each of the following concepts, along with at least one suitable example for each: (i) Fixed-point number representation (ii) round-off error (iii) representation of zero as floating point number (iv) significant digits in a decimal number representation (v) normalized representation of a floating point number (vi) overflow
Calculate a bound for the truncation error in approximating
where
and (fact n) denotes factorial of n
Compute the value of the integral
by using
Rectangular Rule (ii) Trapezoidal Rule and then (iii) Simpson's 1/3 Rule
Regula-falsi method (ii) Newton Raphson method (iii) Bisection method (iv) Secant method
Find out to how many decimal places the value 22/7 is accurate as an approximation of 3.14159265, where the latter is value of, calculated up to 8 places after decimal?