Determine the smallest roots of the following equation:
to three significant digits using
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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?
Express A³f, as a backward difference.
Calculate a bound for the truncation error in approximating
where
and (fact n) denotes factorial of n
If values of the function
find the Lagrange's interpolation polynomial of f(x). Also, find f
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.
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?