Factoring Polynomials

This program finds numerator and denominator polynomials such that their division equals as many terms as possible of the user inputted function.

This program returns the coefficients of the Legendre polynomial P_n, given n. The result is a row vector with powers of x decreasing from left to right (standard MATLAB notation). Like for other polynomials, LegendrePoly(n) can be evaluated at x by typingpolyval(LegendrePoly(n),x).

Given a Legendre polynomial expansion where the coefficients are stored in a column vector, this script computes the expansion in terms of Chebyshev polynomials. Useful for spectral methods.


Platforms: Matlab

Given a Chebyshev polynomial expansion where the coefficients are stored in a column vector, this script computes the expansion in terms of Legendre polynomials. Useful for spectral methods.


Platforms: Matlab

This document is designed to perimiter in a few hours a minimal knowledge of the main features of Matlab. All the basic topics are covered in Matlab:- Generation of vectors and matrices- Handling of arrays and indices- Functions and polynomials- Data Files- Liner algebra in Matlab- Programming-...


Platforms: Matlab

Plots data points and first through sixth degree polynomials. Displays polynomial coefficients and r-squared values in command window. Allows user to choose range. Also allows user to remove trendlines that don't appear to fit.


Platforms: Matlab

This m-file deals with the iterated principal factor method (principal axis factoring) thru the complete data matrix, the latent root criterion, iteration convergence criterion, and uses the varimax factor rotation. It works with an iterative solution for communalities and factor loadings. At...


Platforms: Matlab

This function either displays Zernike polynomials over a circular, hexagonal, elliptical, rectangular or annular shaped pupil, or fits surface data to these pupil shapes. See Mahajan, V.N., G.-m. Dai, "Orthonormal polynomials in wavefront analysis: analytical solution," J. Opt. Soc. Am. A, Vol....


Platforms: Matlab

The Alpert transform is a multiwavelets transform based on orthogonal polynomials. It was originally designed for the resolution of partial differential and integral equations, since it avoids boundary artifact and can be used with an arbitrary sampling.The reference for the numerical...


Platforms: Matlab

Represent a wavefront as a sum of Zernike polynomials using a matrix inversion.This function attempts to solve the a_i's in equation, phi(rho,theta) = SUM(a_i * Z_i(rho,theta), i=1 to M),where the Z_i(rho,theta)'s are the Zernike polynomials from the zernfun.m file, phi is the wavefront to be...


Platforms: Matlab

An iterative QuRecursive method to generate Zernike radial polynomials in matlab. It accepts as input the moment order n and a vector of r values (has been written using a vectorized implementation: multiple r values).


Platforms: Matlab

In image analysis, such as in the field of AFM topography, a standard problem is to fit polynomials of given ORDer to many columns of data, considered as different functions of the same independent variable. POLYFIC solves this problem in a vectorized way (without using loops). In addition to...


Platforms: Matlab

This m-file deals with the iterated principal factor method (principal axis factoring) thru the R-correlation matrix (without the matrix of data), the latent root criterion, iteration convergence criterion, and uses the varimax factor rotation. It works with an iterative solution for...


Platforms: Matlab

Zernike polynomials are orthogonal on the unit circle and are commonly used in optics for phase aberrations. Use zernike_fcn3.m to generate Zernike polynomials. Input includes a vector of the desired polynomials; these do not have to be consecutive. Possible polynomial orderings include: 'noll' =...


Platforms: Matlab

This .zip file contains 3 mfiles for computing the nodes and weights for Legendre Laguerre and Hermite - Gauss Quadrature of any order n.Contrary to most of the files in use, the included files are all based on a symmetrical companion matrix, the eigenvalues of which are always real and...


Platforms: Matlab

This is a very fast and efficient script for nodal-to/from-spectral transforms using chebyshev polynomials on the unit square domain. This version does not require 2^n truncation, but does require the same truncation in both dimension. Users are encouraged to improve and redistribute this script.


Platforms: Matlab

GSP is a graphical user interface which takes x and y points as inputs, along with the order m, then outputs mth order splines between each of the x points. In most cases additional constraints are to be entered as well. Example: Input: x points : [1 2 3 4] y points : [2 7 -1 5] Order : 2 *One...


Platforms: Matlab

The Mandelbrot set has its place in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. The first pictures of it were drawn in 1978 by Brooks and Matelski as part of a study of Kleinian Groups.Mandelbrot...


Platforms: Matlab

This calculator plots orthonormal polynomials for circular, annular, rectangular, hexagonal, and elliptical apertures. FRINGE Zernikes are used for the circular apertures. The annular apertures uses the polynomials derived by V. N. Mahajan, "Zernike annular polynomials for imaging systems with...


Platforms: PHP

Java Algebra System (JAS for short) is an object oriented, type safe and multi-threaded approach to computer algebra. JAS provides a well designed software library using generic types for algebraic computations implemented in the Java programming language. The library can be used as any other...


Platforms: *nix