Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Polynomial Root Finding

Someone recently numerically evaluated this integral:

and got .7285058960783131.

What do you think of their answer?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Polynomial Root Finding

wolfram alpha as well as my hand calculation are yielding same result.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Polynomial Root Finding

Hi;

Computers do not always tell us the truth. We have already seen that  problems can arise when we multiply by a large number, divide by a small number, subtract 2 nearly equal numbers and more.

When we say n = .08 we are implying that we know the number with a certain accuracy. We are claiming

which means  .075 < n < .085

When we say n = .576128 we are implying that we know the number with a certain accuracy. We are claiming

which means  .5761275 < n < .5761285

Putting down the answer .7285058960783131 implies that we know this:

which means .72850589607831305 < .7285058960783131 < .72850589607831315

Are we justified in saying that?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Polynomial Root Finding

I understand your point. I got the value of 0.728505896 after substituting upper and lower limits. There is no estimate of accuracy. I only meant that the results agree up to the digits I got as my answer.As engineers we are even satisfied with 0.7285.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Polynomial Root Finding

Someone else whom was wise gave .728506 as the answer because he was sure of those digits.

A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

It is true in engineering it would be rare to need more than 6 digits but CAS are capable of spitting out millions or even billions of digits. Numerical analysis is one way to determine how reliable those digits that are given are.

The fellow who published .7285058960783131 is making a statement about the accuracy of his answer. We would like to be able to verify it or prove his answer is overoptimistic.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Polynomial Root Finding

Hello;

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Polynomial Root Finding

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Polynomial Root Finding

How do I start working on that integration?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Polynomial Root Finding

What do you want to do with it?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.