Deemed University 2009 A.M.I.E.T.E Electronics

(6)

b. Solve the system of equations by Cholesky method.
(10)

Q.4 a. The population of a town in decimal census were provided in the subsequent table. (6)

Year
: 1921
1931
1941
1951
1961

population in thousand

: 46

66

81

93

101

Estimate the population for the year 1955 using Newtons backward formulae.

b. find the lowest squares polynomial approximation of degree 2 for on [0,1]. (10)

Q.5 a. The subsequent values of the function , are provided (8)
x
10°
20°
30°

1.1585
1.2817
1.3660

construct the quadratic interpolating polynomial that fits the data. Hence obtain
b. obtain the approximate value of the integral by using composite trapezoidal rule with 2,3,5,9 nodes and Romberg Integration. (8)

Q.6 a. Employ Taylors method to find approximate value of y at x=0.2 for the differential formula (8)

b. provided with initial condition y = one at x = 0. obtain y for x = 0.1 by Eulers method. (8)

Q.7 a. presume that f(x) has a minimum in the interval where . Show that the interpolation of f(x) by a polynomial of 2nd degree yields the approximation
for the minimum value of f(x). (8)

b. Prove with the usual notations, that
(i)
(ii) (8)
where = forward difference operator
= Backward difference operator
= Central difference operator
= averaging operator
h = interval of differencing
D = 1st order difference


Q.8 a. Write a C program to obtain a simple root of f(x)=0 using Newton-Raphson method. (10)

b. Evaluate by using Simpsons 3/8 rule. (6)

Q.9 a. Differentiate the followings
(i) call by value and call by reference in C program
(ii) Structures and Unions (8)

b. describe the subsequent terms
(i) Round-off fault
(ii) Truncation fault
(iii) Absolute fault
(iv) Machine epsilon (8)

Earning:   Approval pending.