Regula-falsi method (ii) Newton Raphson method (iii) Bisection method (iv) Secant method
In Computer Oriented Numerical Techniques, various root-finding methods are used to solve nonlinear equations. The Regula-Falsi method or false position method is a bracketing technique that combines the idea of bisection and linear interpolation. It requires two ________ _________ _______ ____ ____ ______ ___ __________ ______.
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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 |
Solve the system of equations
using Gauss elimination method with partial pivoting.
Calculate a bound for the truncation error in approximating
where
and (fact n) denotes factorial of n
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 |
If values of the function
find the Lagrange's interpolation polynomial of f(x). Also, find f
Determine the smallest roots of the following equation:
to three significant digits using
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.