Numerical : Unit I

Numerical methods ..

• is to find the exact solutions of mathematical problems.

• is a study of algorithms that use numerical approximations in solving problems.

• should be accurate and precise enough for particular problems.

A theorem that guaranteed that there is at least a root in the interval is

• Rolle's Theorem

• Extreme Value Theorem

• Intermediate Value Theorem

False Position method is used to solve

• nonlinear equations

• system of linear equations

• quadratic equations

• eigen value problems

Solving nonlinear equations means ..

• finding the root of the functions.

• finding the zero of the functions.

• finding the x value which f(x)=0.

For any given system of linear equations, what are the possible solutions?

• No solution

• Unique solution

• Dual solutions

• Infinite many solutions

The iteration formula for Newton-Raphson method is

• $x_{n+1}=x_n+\frac{f\left(x_n\right)}{f'\left(x_n\right)}$

• $x_{n+1}=x_n-\frac{f\left(x_n\right)}{f'\left(x_n\right)}$

• $x_{n+1}=x_n-\frac{f'\left(x_n\right)}{f\left(x_n\right)}$

• $x_{n+1}=x_n+\frac{f'\left(x_n\right)}{f\left(x_n\right)}$

Newton-Raphson method will fail for the following reasons, except

• $f'\left(x_o\right)\$ is approaching zero

• $f'\left(x_o\right)\$ increases too rapidly

• $x_o$ is too far from the root

• $f\left(x\right)\$ is approaching zero

The following graphs show the situations where Newton-Raphson method may not work, except

• 
• 
• 
• 

What line is used to find the next iteration in Newton-Raphson method?

• Secant

• Normal

• Chord

• Tangent

In Newton-Raphson method, if we want to give our answer correct to 3 decimal places then we need to use how many decimal places in the calculation of the iterations?

• 3 decimal places

• 2 decimal places

• 4 decimal places

• any number of decimal places will do