Find Roots: Explaining the Need for Numerical Methods

[vigintitres]

I am in a numerical methods class, which uses MATLAB and c to do methods like regular falsi and Newton raphson. I should know this, but why do we bother finding the value of x that makes our function evaluate to zero? Is it so that we have some basis as to where to start or stop a certain process or something? I guess I'm really asking why do we need to find roots when you have an equation for some thing that you are analyzing. Thank you

 

[berkeman]

I am in a numerical methods class, which uses MATLAB and c to do methods like regular falsi and Newton raphson. I should know this, but why do we bother finding the value of x that makes our function evaluate to zero? Is it so that we have some basis as to where to start or stop a certain process or something? I guess I'm really asking why do we need to find roots when you have an equation for some thing that you are analyzing. Thank you

Good question. We find roots of the numerator and denominator of a transfer function in order to find where the zeros and poles of the tranfer funtion are located in frequency. This is used in the design of the transfer function, to shape it as a LP, BP, HP, or other function. It also helps us evaluate the stability of the transfer function for various input signals, etc.

http://en.wikipedia.org/wiki/Pole–zero_plot

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[chroot]

Optimization is one of the most important and common tasks in engineering. Optimization means finding the maximal value of something with respect to some variables. To find the maximal value, you take derivatives with respect to your variables, and then find the places where those derivatives are zero.

Thus, finding the zeros of a function is one of the most fundamental mathematical tasks in all engineering.

- Warren

 

[symbolipoint]

chroot said,

finding the zeros of a function is one of the most fundamental mathematical tasks in all engineering.

You can say that again!

Any time a situation can be represented with a rational or polynomial (or who knows what other type of) equation, you may transform that equation into a form of an expression equal to zero. If this is an equation in one variable, then certainly, you are essentially looking for one or more roots as the solution to the unknown variable. Note that the roots may not always be rational; they may not always be Real; but you would still be interested in finding their values. A person does not need to be an engineer in order to accept that. (this topic is in the General Engineering board)