6 messages · Ron Michael, Jorge Ivan Velez, Hans W Borchers +1 more
I need to solve a equation like this : a = b/(1+x) + c/(1+x)^2 + d/(1+x)^3 where a,b,c,d are known constant. Is there any R-way to do that? Thanks in advance
View this message in context: http://www.nabble.com/How-to-solve-following-equation--tp20785063p20785063.html Sent from the R help mailing list archive at Nabble.com.
Assume a = 1. If not set b = b/a, etc. Now use (1) uniroot
f <- function(x) b + c/(1+x) + d/(1+x)^2 - 1 - x uniroot(f, 0:1)
$root [1] 0.8392679 $f.root [1] 3.049818e-05 $iter [1] 3 $estim.prec [1] 6.103516e-05 or multiply through by 1+x and subtract 1 from both sides giving x = b + c/(1+x) + d/(1+x)^2 - 1 and iterate that.
a <- b <- c <- d <- 1
x <- 0
for(i in 1:25) {
+ x <- b + c/(1+x) + d/(1+x)^2 - 1 + print(x) + } [1] 2 [1] 0.4444444 [1] 1.171598 [1] 0.6725419 [1] 0.9553676 [1] 0.7729558 [1] 0.8821595 [1] 0.8135892 [1] 0.8554268 [1] 0.829437 [1] 0.8454056 [1] 0.835527 [1] 0.8416126 [1] 0.837854 [1] 0.8401717 [1] 0.838741 [1] 0.8396236 [1] 0.839079 [1] 0.839415 [1] 0.8392076 [1] 0.8393356 [1] 0.8392566 [1] 0.8393053 [1] 0.8392753 [1] 0.8392938
I need to solve a equation like this : a = b/(1+x) + c/(1+x)^2 + d/(1+x)^3 where a,b,c,d are known constant. Is there any R-way to do that? Thanks in advance -- View this message in context: http://www.nabble.com/How-to-solve-following-equation--tp20785063p20785063.html Sent from the R help mailing list archive at Nabble.com.
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
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I need to solve a equation like this : a = b/(1+x) + c/(1+x)^2 + d/(1+x)^3 where a,b,c,d are known constant. Is there any R-way to do that?
Multiplying this expression with (1+x)^3 leads to a polynomial equation.
I would certainly recommend the 'PolynomF' package here:
----
# install.packages("PolynomF")
library("PolynomF")
options(digits=16)
x <- polynom()
a <- b <- c <- d <- 1
p <- a*(1+x)^3 - b*(1+x)^2 - c*(1+x) - d
p
# -2 + 2*x^2 + x^3
solve(p)
# [1] -1.419643377607080-0.6062907292072i
# -1.419643377607080+0.6062907292072i
# [3] 0.839286755214161+0.0000000000000i
----
The solution x0 = 0.839286755214161 is correct up to the last digit, as can be
verified by using a computer algebra system. This also shows that Ryacas is
quite exact in this task.
Hans Werner
Gabor Grothendieck <ggrothendieck <at> gmail.com> writes:
Assume a = 1. If not set b = b/a, etc. Now use (1) uniroot
f <- function(x) b + c/(1+x) + d/(1+x)^2 - 1 - x uniroot(f, 0:1)
$root [1] 0.8392679 $f.root [1] 3.049818e-05 $iter [1] 3 $estim.prec [1] 6.103516e-05 or multiply through by 1+x and subtract 1 from both sides giving x = b + c/(1+x) + d/(1+x)^2 - 1 and iterate that.
a <- b <- c <- d <- 1
x <- 0
for(i in 1:25) {
+ x <- b + c/(1+x) + d/(1+x)^2 - 1 + print(x) + } [1] 2 [1] 0.4444444 [1] 1.171598 [1] 0.6725419 [1] 0.9553676 [1] 0.7729558 [1] 0.8821595 [1] 0.8135892 [1] 0.8554268 [1] 0.829437 [1] 0.8454056 [1] 0.835527 [1] 0.8416126 [1] 0.837854 [1] 0.8401717 [1] 0.838741 [1] 0.8396236 [1] 0.839079 [1] 0.839415 [1] 0.8392076 [1] 0.8393356 [1] 0.8392566 [1] 0.8393053 [1] 0.8392753 [1] 0.8392938 On Mon, Dec 1, 2008 at 9:47 PM, RON70 <ron_michael70 <at> yahoo.com> wrote:
I need to solve a equation like this : a = b/(1+x) + c/(1+x)^2 + d/(1+x)^3 where a,b,c,d are known constant. Is there any R-way to do that? Thanks in advance -- View this message in context:
http://www.nabble.com/How-to-solve-following-equation--tp20785063p20785063.html
Sent from the R help mailing list archive at Nabble.com.
______________________________________________ R-help <at> r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
______________________________________________ R-help <at> r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Thanks for this reply, However I am interested to know why I need to modify my function to a=1? Regards,
Assume a = 1. If not set b = b/a, etc. Now use (1) uniroot
f <- function(x) b + c/(1+x) + d/(1+x)^2 - 1 - x uniroot(f, 0:1)
$root [1] 0.8392679 $f.root [1] 3.049818e-05 $iter [1] 3 $estim.prec [1] 6.103516e-05 or multiply through by 1+x and subtract 1 from both sides giving x = b + c/(1+x) + d/(1+x)^2 - 1 and iterate that.
a <- b <- c <- d <- 1
x <- 0
for(i in 1:25) {
+ x <- b + c/(1+x) + d/(1+x)^2 - 1 + print(x) + } [1] 2 [1] 0.4444444 [1] 1.171598 [1] 0.6725419 [1] 0.9553676 [1] 0.7729558 [1] 0.8821595 [1] 0.8135892 [1] 0.8554268 [1] 0.829437 [1] 0.8454056 [1] 0.835527 [1] 0.8416126 [1] 0.837854 [1] 0.8401717 [1] 0.838741 [1] 0.8396236 [1] 0.839079 [1] 0.839415 [1] 0.8392076 [1] 0.8393356 [1] 0.8392566 [1] 0.8393053 [1] 0.8392753 [1] 0.8392938 On Mon, Dec 1, 2008 at 9:47 PM, RON70 <ron_michael70 at yahoo.com> wrote:
I need to solve a equation like this : a = b/(1+x) + c/(1+x)^2 + d/(1+x)^3 where a,b,c,d are known constant. Is there any R-way to do that? Thanks in advance -- View this message in context: http://www.nabble.com/How-to-solve-following-equation--tp20785063p20785063.html Sent from the R help mailing list archive at Nabble.com.
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
View this message in context: http://www.nabble.com/How-to-solve-following-equation--tp20785063p20817656.html Sent from the R help mailing list archive at Nabble.com.
You don't. This was just to make the presentation simpler.
Thanks for this reply, However I am interested to know why I need to modify my function to a=1? Regards, Gabor Grothendieck wrote:
Assume a = 1. If not set b = b/a, etc. Now use (1) uniroot
f <- function(x) b + c/(1+x) + d/(1+x)^2 - 1 - x uniroot(f, 0:1)
$root [1] 0.8392679 $f.root [1] 3.049818e-05 $iter [1] 3 $estim.prec [1] 6.103516e-05 or multiply through by 1+x and subtract 1 from both sides giving x = b + c/(1+x) + d/(1+x)^2 - 1 and iterate that.
a <- b <- c <- d <- 1
x <- 0
for(i in 1:25) {
+ x <- b + c/(1+x) + d/(1+x)^2 - 1 + print(x) + } [1] 2 [1] 0.4444444 [1] 1.171598 [1] 0.6725419 [1] 0.9553676 [1] 0.7729558 [1] 0.8821595 [1] 0.8135892 [1] 0.8554268 [1] 0.829437 [1] 0.8454056 [1] 0.835527 [1] 0.8416126 [1] 0.837854 [1] 0.8401717 [1] 0.838741 [1] 0.8396236 [1] 0.839079 [1] 0.839415 [1] 0.8392076 [1] 0.8393356 [1] 0.8392566 [1] 0.8393053 [1] 0.8392753 [1] 0.8392938 On Mon, Dec 1, 2008 at 9:47 PM, RON70 <ron_michael70 at yahoo.com> wrote:
I need to solve a equation like this : a = b/(1+x) + c/(1+x)^2 + d/(1+x)^3 where a,b,c,d are known constant. Is there any R-way to do that? Thanks in advance -- View this message in context: http://www.nabble.com/How-to-solve-following-equation--tp20785063p20785063.html Sent from the R help mailing list archive at Nabble.com.
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
-- View this message in context: http://www.nabble.com/How-to-solve-following-equation--tp20785063p20817656.html Sent from the R help mailing list archive at Nabble.com.
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.