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 thousands) | | -------- | --------------------------- | | _______ __________ _________ ________ ___ ______ ________ _____.
___ __________ ________ __________ ____ ________.
__________ _________ _______ _________ ______ ___.
________ ______ _______ _____ _____ ____ ______ ____ _____.
____ ____ __________ _______ _________ _________ ____ __________ ___ ________ ____ ____.
_______ _______ ________ ______ ___ ______ ______ ____ _________.
_________ _________ _____ __________ _______.
__________ ___ _________ ____ __________ ____ _____ _____ _______.
_____ ____ __________ __________ _____.
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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
Explain what is the role of interpolation in solving numerical problems?
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.
Regula-falsi method (ii) Newton Raphson method (iii) Bisection method (iv) Secant method
If values of the function
find the Lagrange's interpolation polynomial of f(x). Also, find f
Find the values of the first and second derivatives of f(x) at x = 76 from the following table. Use 0(h2 ) forward difference method. Also, find Truncation Error (TE) and actual errors.
| x: | 76 | 81 | 86 | 91 |
| f(x) : | 5.3147 | 5.4346 | 5.5637 | 5.6629 |
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?