NUMERICAL METHODS

The convergence of which of the following method is sensitive to starting value?

• False position

• Gauss seidal method

• Newton-Raphson method

• All of these

Newton-Raphson method is used to find the root of the equation x2 - 2 = 0

If iterations are started from - 1, then iterations will be

• converge to -1

• converge to √2

• converge to -√2

• No converge

Which of the following statements applies to the bisection method used for finding roots of functions?

• Converges within a few iterations

• Guaranteed to work for all continuous functions

• Is faster than the Newton-Raphson method

• Requires that there be no error in determining the sign of the function

We wish to solve x2 - 2 = 0 by Newton Raphson technique. If initial guess is x0 = 1.0, subsequent estimate of x (i.e. x1) will be

• 1.414

• 1.5

• 2.0

• None of these

Using Newton-Raphson method, find a root correct to three decimal places of the equation x3 - 3x - 5 = 0

• 2.275

• 2.279

• 2.222

• None of these

In the Gauss elimination method for solving a system of linear algebraic equations, triangularzation leads to

• Diagonal matrix

• Lower triangular matrix

• Upper triangular matrix

• Singular matrix

If Δf(x) = f(x+h) - f(x), then a constant k, Δk equals

• 1

• 0

• f(k)- f(0)

• f(x + k) - f(x)

Double (Repeated) root of

4x3- 8x2- 3x + 9 = 0 by Newton-raphson method is

• 1.4

• 1.5

• 1.6

• 1.55

Using Bisection method, negative root of x3 - 4x + 9 = 0 correct to three decimal places is

• -2.506

• -2.706

• - 2.406

• None of these

Four arbitrary points (x1, y1), (x2, y2), (x3, y3),(x4, y4) are given in the x, y-plane. Using the method of least squares, if regressing y upon x gives the fitted line y = ax + b; and regressing y upon x gives the fitted line y + ax + b; and regressing x upon y gives the fitted line

x = cy + d, then

• Two fitted lines must coincide

• Two fitted lines need not coincide

• It is possible that ac = 0

• A must be 1/c