search for: polynomial

Hi, I would like to know whether there exist algorithms to compute the coefficients or, at least, the degree of the minimal polynomial of a square matrix A (over the field of complex numbers)? I don't know whether this would require symbolic computation. If not, has any of the algorithms been implemented in R? Thanks very much, Ravi. P.S. Just for the sake of completeness, a minimal polynomial is a monic polynomia...

...thing without much luck, and have scoured help-pages, but nothing has come up. Here it is: I have a matrix (m) of approx 40,000 rows and 3 columns, filled with numbers. I would like to convert the contents of this matrix into another matrix (m_p), where the numbers of (m) have been coerced into a polynomial - using a function called "as.polynomial()" from the package (polynom). Each row of (m) contains 3 terms to be made into a polynomial in the equivalent row of (m_p). I have tried a coupe of things: ------------------------------ 1. Using apply() m_p<-apply(m, 2, as.polynomial) Here...

Hi, I want find all roots for the following polynomial : a <- c(-0.07, 0.17); b <- c(1, -4); cc <- matrix(c(0.24, 0.00, -0.08, -0.31), 2); d <- matrix(c(0, 0, -0.13, -0.37), 2); e <- matrix(c(0.2, 0, -0.06, -0.34), 2) A1 <- diag(2) + a %*% t(b) + cc; A2 <- -cc + d; A3 <- -d + e; A4 <- -e fn <- function(z) { y <-...

Hi all, We know that Hermite polynomial is for Gaussian, Laguerre polynomial for Exponential distribution, Legendre polynomial for uniform distribution, Jacobi polynomial for Beta distribution. Does anyone know which kind of polynomial deals with the log-normal, Student抯 t, Inverse gamma and Fisher抯 F distribution? Thank you in advance!...

I am trying to understand what is the difference between linear and polynomial kernel: linear: u'*v polynomial: (gamma*u'*v + coef0)^degree It would seem that polynomial kernel with gamma = 1; coef0 = 0 and degree = 1 should be identical to linear kernel, however it gives me significantly different results for very simple data set, with linea...

Hi everybody! I'm looking some way to do in R a polynomial fit, say like polyfit function of Octave/MATLAB. For who don't know, c = polyfit(x,y,m) finds the coefficients of a polynomial p(x) of degree m that fits the data, p(x[i]) to y[i], in a least squares sense. The result c is a vector of length m+1 containing the polynomial coefficients in descen...

I wonder how one in R can fit a 3rd degree polynomial to some data? Say the data is: y <- c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18, 11.32) x <- seq(3.75, 6, 0.25) And resulting degrees of polynomial are: 5.8007 -91.6339 472.1726 -774.2584 THanks in advance! -- Jonas Malmros Stockholm University Stockholm, Sweden

I'm trying to find a way to fit a polynomial of degree n in x and y to a set of x, y, and z data that I have and obtain the coefficients for the terms of the fitted polynomial. However, when I try to use the surf.ls function I'm getting odd results. > x <- seq(0, 10, length=50) > y <- x > f <- function (x, y) {x^2 +...

Hey all, I'm performing polynomial regression. I'm simulating x values using runif() and y values using a deterministic function of x and rnorm(). When I perform polynomial regression like this: fit_poly <- lm(y ~ poly(x,11,raw = TRUE)) I get some NA coefficients. I think this is due to the high correlation between say x...

Hello, i'm fairly familiar with R and use it every now and then for math related tasks. I have a simple non polynomial function that i would like to approximate with a polynomial. I already looked into poly, but was unable to understand what to do with it. So my problem is this. I can generate virtually any number of datapoints and would like to find the coeffs a1, a2, ... up to a given degree for a polynomial a1x^...

Dear R-users, I learned today that there exists an interesting topic in numerical analysis names "best polynomial approximation" (BSA). Given a function f the BSA of degree k, say pk, is the polynomial such that pk=arginf sup(|f-pk|) Although given some regularity condition of f, pk is unique, pk IS NOT calculated with least square. A quick google tour show a rich field of research and many algorithms...

...ease bear with me. I've just spent some time fitting poly functions to time series data in R using lm() and predict(). I want to analyze the functions once I've fit them to the various data I'm studying. However, after pulling the first function into Octave (just by plotting the polynomial function using fplot() over the same x interval as my original data) I was surprised to see that the scale and y values were vastly different than the ones I have in R. The basic shape of the polynomial over the same interval looks similar in both Octave and R, but the y values are all di...

Dear list, This is quite a specific question requiring the package orthopolynom. This package provides a nice implementation of the Legendre polynomials, however I need the associated Legendre polynomial which can be readily expressed in terms of the mth order derivative of the corresponding Legendre polynomial. (For the curious, I'm trying to calculate spherical harmonics [*]). Because legendre.polynomials(l) returns a list of Legendre...

Dear all, Can any one tell me how can i perform Orthogonal Polynomial Regression parameter estimation in R? -------------------------------------------- Here is an "Orthogonal Polynomial" Regression problem collected from Draper, Smith(1981), page 269. Note that only value of alpha0 (intercept term) and signs of each estimate match with the result obtaine...

Hello [R]-help I am trying to find > a package where you can do ANOVA based trend analysis on grouped data > using orthogonal polynomial contrasts coefficients, for unequally > spaced factor levels. The closest hit I've had is from this web site: >(http://webcache.googleusercontent.com/search?q=cache:xN4K_KGuYGcJ:www.datavis.ca/sasmac/orpoly.html+Orthogonal+polynomial >l but I cannot find this package or anything like...

Hi All, I need to evaluate a series expansion using Legendre polynomials. Using the 'orthopolinom' package I can get a list of the first n Legendre polynomials as character strings. > library(orthopolynom) > l<-legendre.polynomials(4) > l [[1]] 1 [[2]] x [[3]] -0.5 + 1.5*x^2 [[4]] -1.5*x + 2.5*x^3 [[5]] 0.375 - 3.75*x^2 + 4.375*x^4 But I can...

...e Gram-Charlier series expansion to model some data. To do that, I need functions to: 1) Calculate 'n' moments from given data 2) Transform 'n' moments to 'n' central moments, or 3) Transform 'n' moments to 'n' cumulants 4) Calculate a number of Hermite polynomials Are there R-functions to do any of the above? (mean, sd and cum3 are very limited) Thank you for your help, Augusto -------------------------------------------- Augusto Sanabria. MSc, PhD. Mathematical Modeller Risk Research Group Geospatial & Earth Monitoring Division Geoscience Austr...

How can ordinary polynomial coefficients be calculated from an orthogonal polynomial fit? I'm trying to do something like find a,b,c,d from lm(billions ~ a+b*decade+c*decade^2+d*decade^3) but that gives: "Error in eval(expr, envir, enclos) : Object "a" not found" > decade <- c(1950, 1960, 1...

Hi, Suppose I have the following lines at the end of a function: answer <- c(2, 1, 0, 4, 5) # In fact, answer will be generate in my # function print(answer) # Print the answer # Now, find the best fitted n degree polynomial print(paste("The best fit is with", which.min(answer) - 1, "-degree polynomial")) this will return: [1] 2 1 0 4 5 [1] "The best fit is with 2 -degree polynomial" Two questions: 1) How can I supress the [1] in the second line in the output? 2) T...

Dear Thomas, Unfortunately, I do not know if any packages implement this functionality. Though, it is a topic that interests me. Unlike the "classic discriminant", I prefer to work with the reduced polynomial. This "discriminant" is generalizable to a superset of Chebysev polynomials (which I called Cardano-polynomials). x^3 - 3*c*x - 2*d = 0 x^5 - 5*c*x^3 + 5*c^2*x - 2*d = 0 x^7 - 7*c*x^5 + 14*c^2*x^3 - 7*c^3*x - 2*d = 0 discr = d^2 - c^n, where n = 3 for the degree 3 polynomial; The beauty...