NUMERICAL ANALYSIS — DU B.Sc. (Hons) Physics Previous Year Question Papers

(a) The error in the measurement of the area of a circle is not allowed to exceed 0.1%. How accurately should the diameter be measured? (b) Find the eigenvalues of the matrix i -2 Foin (c) Given A = 166 78 37 ,, show that A is an ill-conditioned matrix. (d) Give a geometrical interpretation of the trapezoidal rule. (e) State the minimax theorem. (f) State Runge-Kutta fourth-order formula 2. (a) Solve the following equations by LU decomposition method. (b) Solve by following equation by Gauss-Seidel method: 3. (a)Find the largest eigen value and the corresponding eigen vector of the following matrix using power method taking as the initial approximation for the eigen vector. (Compute Five iterations) (b) Solve the following equations using the Gauss elimination method 4. (a) Using Newton's divided difference formula, calculate the value of f(6) from the following data: (b) The value of x and y are given as below: Using Lagrange interpolation, find the value of y at x = 10 (7) 5. (a) Evaluate S* e* dx using Simpson's - rule taking step size h = 1 (6) (b) Solve dy = -2xy2 with y(O)=1 and h=0.2 on the interval [0, 1], using Runge-Kutta fourth order method. (9)