Re: [R] Solving 100th order equation

Spencer Graves Sat, 24 May 2008 08:21:53 -0700

Consider the following:

library(polynomial)
p100 <- polynomial(1:101)
s100 <- solve(p100)
p100r <- 101*poly.calc(s100, tol=.Machine$double.eps)
max(abs(coef(p100r)-(1:101)))
550767713

For order 2, it worked perfectly:

(p2 <- polynomial(1:3))
(s2 <- solve(p2))
(p2r <- 3*poly.calc(s2))
max(abs(coef(p2r)-1:3))
0

For order 50, it clearly had some problems:

p50 <- polynomial(1:51)
s50 <- solve(p50)
p50r <- 3*poly.calc(s50)
max(abs(coef(p50r)-1:3))
max(abs(coef(p50r)-1:3))
[1] 2.823529

To find the theoretical method, the ultimate reference is thecode. Reading "polynom:::solve.polynomial" reveals that this passes anappropriate matrix to 'eigen'.Hope this helps.Spencer


Shubha Vishwanath Karanth wrote:

Was also wondering which theoretical method is used to solve this problem?

Thanks,
Shubha Karanth | Amba Research

Ph +91 80 3980 8031 | Mob +91 94 4886 4510Bangalore * Colombo * London * New York * San José * Singapore * www.ambaresearch.com


-----Original Message-----

From: Gabor Grothendieck [mailto:[EMAIL PROTECTED]Sent: Saturday, May 24, 2008 6:13 PM

To: Peter Dalgaard
Cc: Shubha Vishwanath Karanth; [EMAIL PROTECTED]; Duncan Murdoch
Subject: Re: [R] Solving 100th order equation

On Sat, May 24, 2008 at 8:31 AM, Peter Dalgaard
<[EMAIL PROTECTED]> wrote:

Shubha Vishwanath Karanth wrote:

To apply uniroot I don't even know the interval values... Does numerical
methods help me? Or any other method?

Thanks and Regards,
Shubha

-----Original Message-----
From: Duncan Murdoch [mailto:[EMAIL PROTECTED] Sent: Saturday, May 24,
2008 5:08 PM
To: Shubha Vishwanath Karanth
Subject: Re: [R] Solving 100th order equation

Shubha Vishwanath Karanth wrote:

Hi R,


I have a 100th order equation for which I need to solve the value for x.
Is there a package to do this?


For example my equation is:


(x^100 )- (2*x^99) +(10*x^50)+.............. +(6*x ) = 4000


I have only one unknown value and that is x. How do I solve for this?

uniroot() will find one root.  If you want all of them, I don't know what
is available.

Duncan Murdoch

polyroot() is built for this, but it stops at 48th degree polynomials, at
least as currently implemented. Not sure that it (or anything else) would be
stable beyond that limit. YACAS perhaps?


Unfortunately yacas does not seem to be able to handle it:

library(Ryacas)
x <- Sym("x")
Solve((x^100 )- (2*x^99) +(10*x^50)+(6*x ) - 4000 == 0, x)

[1] "Starting Yacas!"
expression(list())

Simpler one works ok:

Solve(x^2 - 1, x)

expression(list(x == 1, x == -1))
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Re: [R] Solving 100th order equation

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