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## #176 2016-06-20 14:36:09

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

``````>>> n = 50
>>> a = 1241.0
>>> while n != 20:
...     n -= 1
...     a = ((1.0/n) - a)/8.0
...
>>> a
0.005585251327875914``````

'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.

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## #177 2016-06-20 14:55:29

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

So we have the recurrence

But of course it is ill conditioned and therefore needs to be run backwards.

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.

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## #178 2016-06-20 15:13:18

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

Are you talking to me?

'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.

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## #179 2016-06-20 15:15:27

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

Sorry, I was solving the integral that anonimnystefy provided.

I did notice your nice solution in procedural style.

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.

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## #180 2016-06-20 23:18:57

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

'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.

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## #181 2016-06-20 23:31:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

You need to go one more. I would have put that n -=1 below the a = ((1.0/n) - a)/8.0

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.

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## #182 2016-06-21 03:59:08

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

The classic off-by one error

'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.

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## #183 2016-06-21 11:04:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

Anything else?

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.

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## #184 2016-06-21 15:14:58

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

Is 0.005317989376992687 better?

'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.

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## #185 2016-06-21 15:41:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

In numerical work you either know the answer or you do not. You can answer that question for yourself.

Anything further to discuss on NA?

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.

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## #186 2016-06-21 16:45:22

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Polynomial Root Finding

{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.}

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## #187 2016-06-21 16:53:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

Hi;

.005317989376992687

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.

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## #188 2016-06-21 19:22:46

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

bobbym wrote:

In numerical work you either know the answer or you do not. You can answer that question for yourself.

Anything further to discuss on NA?

How do I chek the value of a_20?

'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.

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## #189 2016-06-21 19:35:06

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Polynomial Root Finding

{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.}

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## #190 2016-06-21 20:00:09

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

The geometry of the integrand does not support Simpsons well but I tried it anyway. It got a pretty close answer.

To check, enter this at Wolfram Alpha:

NIntegrate[x^20/(x + 8), {x, 0, 1}, WorkingPrecision -> 20]

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.

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## #191 2016-06-23 22:47:56

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Polynomial Root Finding

I think I had made some mistake in integration by Simpson rule It comes out to be 0.005318031 with same 100 divisions.

{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.}

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## #192 2016-06-24 02:53:49

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

Agnishom wrote:
bobbym wrote:

In numerical work you either know the answer or you do not. You can answer that question for yourself.

Anything further to discuss on NA?

How do I chek the value of a_20?

'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.

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## #193 2016-06-24 04:30:15

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

Hi;

You are not convinced?

I use the 2 way method to check numerical work.

I was amazed when I got it to work too. Perhaps, a bit of work on the integrand first, would be safer.

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.

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## #194 2016-06-24 12:21:13

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

How did you check the value of a[20] here?

'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.

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## #195 2016-06-24 12:36:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

1) I have the analytical answer.

2) I evaluated the integral numerically.

3) I ran the recurrence in the backward direction.

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.

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## #196 2016-06-25 02:29:21

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

'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.

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## #197 2016-06-25 03:06:44

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

Hmmm, you have the mighty M, it is more powerful than all the m's put together. It is wiser than the Oracle at Delphi. You do not know how to get it?

where

is the HurwitzLerchPhi function.

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.

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## #198 2016-06-25 12:53:35

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

Dioes the recurrence problem you gave me come from the integral?

'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.

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## #199 2016-06-25 13:07:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Polynomial Root Finding

Of couse it does!

http://www.mathisfunforum.com/viewtopic … 57#p384157

Post #177. You should see that a minor change produces the recurrence of this thread.

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.

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## #200 2016-06-25 17:39:52

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

### Re: Polynomial Root Finding

Okay...

What's next?

'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.

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