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?
We are given the linear system: $$ \begin{aligned} 5x_1 - 5x_2 - x_3 &= -8 ______ ___ __________ __________ _____.
_______ ______ _____ ______ ________ _______.
____ _________ _______ ____ ____ ______ ____ ________ _______ ____ _______ ________.
______ ___ ___ _______ ______ _____ _____ ______.
__________ ____ ___ _______ ____ ______ ________.
______ ____ ___ _______ ___ _________.
______ ________ ________ _______ _____ ________ __________ __________ __________ ___.
_________ _________ ____ __________ __________ ___.
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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 |
Obtain Approximate the value of (3.7)-1 using first three terms of Taylor's series expansion.
Explain with suitable example that in computer arithmatics (i.e., numbers represented in computer, with +, -, , / as implemented in a computer) the multiplication operation() may not be distributive over plus (+), i.e. may not be true for some computer numbers a, b and c
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?
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 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?
Compute the value of the integral
by using
Rectangular Rule (ii) Trapezoidal Rule and then (iii) Simpson's 1/3 Rule