# Polynomials and Numerical Analysis

##### Member
Why polynomials are used in numerical analysis?

#### Bacterius

##### Well-known member
MHB Math Helper
Re: Numerical analysis

Why polynomials are used in numerical analysis?
[JUSTIFY]This is a very broad question.. I suppose because their structure is relatively straightforward and well-understood, and they are flexible yet easy to manipulate (it's trivial to differentiate/integrate/add/multiply polynomials, they are well-behaved with respect to numerical approximation methods, we know exactly when they cross the x-axis, we can easily find their minima and maxima, they work the same in the complex plane, and so on..) Can you be more specific?[/JUSTIFY]

#### chisigma

##### Well-known member
Re: Numerical analysis

Why polynomials are used in numerical analysis?
Polynomial are based on the elentary operators of sum and multiplication, the most feasible for humans and computers... that's why N.A., the scope of which is to solve numerically problems, is pratically based on polynomials...

Kind regards

$\chi$ $\sigma$

#### Ackbach

##### Indicium Physicus
Staff member
Re: Numerical analysis

I think another reason why numerical analysis uses polynomials is that they are dense in some very large function spaces. That means (in case you weren't already aware of what it means) that you can approximate a very large number of functions with polynomials. This is quite useful in differential equations, with series methods like Frobenius. Indeed, the motion of, say, a round drum head when you hit it can be modeled using Bessel functions, which are written as an infinite sum of polynomials.