Enlist various methods for solving linear algebraic equations.
[3 marks]Explain intermediate value property theorem.
[4 marks]Round off the numbers 658740 and 67.36584 to four significant figures and compute Ea, Er, Ep in each case.
[7 marks]Explain error propagation in addition and subtraction operation.
[3 marks]Define Inherent, Rounding off and Truncation error.
[4 marks]Find a root of the equation x3 −2x−5 = 0, using the method of false position correct to three decimal places.
[7 marks]Find the root of the equation xex = cosx using the secant method correct to four decimal places.
[7 marks]Explain Descarte’s rule of sign with example.
[3 marks]Explain iterative method to improve accuracy of an ill conditioned equation.
[4 marks]5 Find the eigen-values and eigenvectors of the matrix[ ].12
[7 marks]Write short note on iterative methods.
[3 marks]Define Eigen values and Eigen vectors.
[4 marks]Using the Gauss elimination method, solve the equations: x+2y+3z−u = 10;2x +3y−3z−u = 1; 2x −y+2z+3u = 7;3x+2y−4z+3u =
[2 marks]Write an algorithm for Newton-Raphson method.
[3 marks]Define curve fitting. What is meant by the curve of best fit?
[4 marks]Solve, by Jacobi’s iteration method, the equations 20x +y−2z = 17;3x +20y−z = −18;2x −3y+20z = 25
[7 marks]Write an algorithm for Newton’s forward interpolation formula.
[3 marks]Find the missing term is the table: x: 2 3 4 5 y: 45.0 49.2 54.1 ? 67.4
[6 marks]Find the polynomial f (x) by using Lagrange’s formula and hence find f(3) for x 0 1 2 f(x) 2 3 12 1471
[5 marks]Write an algorithm for trapezoidal rule.
[3 marks]Use Simpson’s 1/3rd rule to find ∫ 0.6 e−x2 dx by taking seven04 ordinates.
[ marks]Find the least squares fit of the form y = a +a x2 to the01 following data x: -1 0 1 y: 2 5 3 0
[2 marks]Write an algorithm of Simpson’s 3/8 rule.
[3 marks]Discuss in brief about boundary problems.
[4 marks]Using Euler’s method, find an approximate value of y corresponding to x = 1,given thatdy⁄dx = x+y and y = 1 when x = 0.
[7 marks]