1) Explain different types of numerical errors with suitable examples. 2) Define the following terms: Absolute Error, Relative Error, and Blunders.
[3 marks]Find the dominant Eigen value and the corresponding Eigen vector of the following matrix using Power method :
[7 marks]Use Bisection method to find the root of the equation x3 – 5x + 1 = 0, in the interval [2, 3], correct upto three decimal places.
[7 marks]Graphically explain the Newton-Raphson method to find the root of the equation f(x) = 0.
[7 marks]Find the root of the equation x3 + 3x2 + 27x – 25 = 0 using Birge-Vieta method (Take r0 = 0.5). Perform only three iterations.
[7 marks]Solve the following system of equations using Gauss elimination method 2x + y + z =10 3x +2y+3z=18 x + 4y +9z=16
[7 marks]Write a well commented program for Secant method. Also explain it in detail.
[7 marks]From the following table, find Pwhen t = 142 °Cand 175 °C, using appropriate Newton’s Interpolation formula. Temp (t) °C : 140 150 160 170 180 Pressure (P) kgf/cm2 : 3.685 4.854 6.302 8.076 10.225
[7 marks]Write an algorithm for Gauss-Seidal Method.
[7 marks]Derive the formula for Newton’s Divided Difference Interpolating Polynomial.
[7 marks]Given the following data find the cubic spline equations for the 4 intervals x 1 2 3 4 f(x) 6 -3 6 2 -6 Find the value of f(x) at x = 3.8
[5 marks]Using Lagrange’s interpolation formula, find the value of y when x = 3, from the following data : x : 0 1 2 4 y : 0 16 48 88 0 Page 1 of
[2 marks]The function y = sin(x) is tabulated below. Find the value of Cos(1.74) and Cos(1.84) using interpolation technique. x 1.70 1.74 1.78 1.82 1.86 sin(x) 0.9917 0.9857 0.9782 0.9691 0.9585
[7 marks]Fit a second degree parabola of the form y = ax2 + bx +c to the following data by the method of least squares x : 1 2 3 4 y : 5 12 26 60 97
[5 marks]Giving suitable examples, explain approximation of functions by Taylor series.
[7 marks]7
[ marks]Discuss the differences between false-position method and secant method. Also mention convergence criteria for successive approximation method. Illustrate selection of proper function with suitable example. Page 2 of
[2 marks]