Express A³fi as a central difference.
In Computer Oriented Numerical Techniques, the operator $A^3 f_i$ represents the third forward difference applied to a function $f$ at point $i$. To express this as a central difference, we rewrite it using central _____ ____ ___ ___ ____ ____ ________ ______ ______.
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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.
Express A³f, as a backward difference.
Regula-falsi method (ii) Newton Raphson method (iii) Bisection method (iv) Secant method
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 |
Solve the system of equations
using Gauss elimination method with partial pivoting.
Compute the value of the integral
by using
Rectangular Rule (ii) Trapezoidal Rule and then (iii) Simpson's 1/3 Rule
Perform four iterations (rounded to four decimal places) using
(i) Jacobi Method and
(ii) Gauss-Seidel method,
for the following system of equations
. The exact solution is (1, 2, 3)T. Which method gives better approximation to the exact solution?