Software Listing: Polynomial

These functions show some advances about MPF (Matrix Polynomial Fraction) using for represent multivariable models and design multivariable control system..

  • Platform: Matlab, Scripts

POLYCOMP Polynomial composition R = POLYCOMP(P,Q) returns the composition of Q(P(x)) given polynomials P and Q with coefficients in descending order. If Q is a scalar, with value N, it assumes shorthand notation for Q(x)=x^N. Output is a polynomial with coefficients in descending order. Example: % p(x) = 2x+1 % q(x) = 2x^2 + 4x + 3 % q(p(x)) = 2[2x+1]^2 + 4[2x+1] + 3 p=[2 1] q=[2 4 3] r=polycomp(p,q) % p(x) = 2x+1 % q(x) = x^3 (scalar, shorthand notation) % q(p(x)) = [2x+1]^3 p=[2 1] q=3 r=polycomp(p,q).

  • Platform: Matlab, Scripts

As its name suggests, Non-linear arithmetic property checker via Bernstein polynomial is a handy tool for checking certain polynomial constraint problems.

You can use the examples that the application comes with or create your own by specifying the variables, the coefficient of the polynomial and the bound for each variable.

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  • Platform: WinOther

UltimaCalc is a scientific and mathematical calculator designed to occupy minimum screen area, making it immediately available for use. UltimaCalc can stay on top of other windows. Type a calculation as plain text, evaluate it, maybe edit it and re-calculate. Has a comprehensive context-sensitive help system. Calculates to 38 digit precision. The display can be limited to just 8, 12 or 16 digits, and digits grouped for readability. Two 'scientific' view modes show numbers always in exponent format. The 'engineering' mode uses suffixes such as k (kilo) and M (mega). View results in hexadecimal and as ratios.

  • Publisher: UltimaCalc
  • Date: 14-06-2006
  • Size: 3112 KB
  • Platform: Win2000, Windows Server, WinOther

A given polynomial p(x) is transformed into a rational function r(x). The poles and residues of the derived rational function are found to be equivalent to the roots and multiplicities of the original polynomial. p(x) = Given polynomial = PROD[k=1:K]{(x - z_k)^m_k} d(x) = (d/dx)p(x) g(x) = GCD(p(x),d(x)) u(x) = p(x)/g(x) w(x) = (d/dx)u(x) v(x) = d(x)/g(x) r(x) = v(x)/u(x) = SUM[k=1:K]{m_k/(x - z_k)} Thus, the roots z_k are computed from solving the simple-root polynomial u(x)=0, instead of the original multiple-root polynomial p(x)=0; and the multiplicities m_k are determined as the partial fraction expansion coefficients of the derived rational function r(x)=v(x)/u(x), z_k = Roots(u(x)), k=1,K m_k = v(z_k)/w(z_k), k=1,K In addition, re-constructing a polynomial pz(x) from the computed z_k and m_k, the overall deviation...

  • Platform: Matlab, Scripts

Often, measured data is comprised of N sampled values of z, evaluated at N locations (x,y). With this function, you can calculate the coefficients of the best-fit x,y polynomial using a linear least squares approximation. You can use this function if you have a set of N data triplets x,y,z, and you want to find a polynomial f(x,y) of a specific form (i.e. you know the terms you want to include (e.g. x^2, xy^3, constant, x^-3, etc.) in your fitting polynomial..

  • Publisher: Thomas
  • Date: 06-01-2013
  • Size: 10 KB
  • Platform: Matlab, Scripts

Routh-Hurwitz stability criterion identifies the conditions when the poles of a polynomial cross into the right hand half plane and hence would be considered as unstable in control engineering..

  • Platform: Matlab, Scripts

The code implements the so called Faddeev-Leverrier algorithm to compute the coefficients of the characteristic polynomial of a given matrix and to get the inverse of the matrix without extra cost..

  • Publisher: Yi Cao
  • Date: 18-05-2013
  • Size: 10 KB
  • Platform: Matlab, Scripts

Given the coefficients of the characteristic polynomial the Routh-Hurwitz array is created and printed. Additionally, this method shows some results from the array relating to the stability of the system..

  • Platform: Matlab, Scripts

RA=ROUTH(R,EPSILON) returns the symbolic Routh array RA for polynomial. The following special cases are considered: 1) If the first element of a row becomes zero OR 2) If one encounters a row full of zeros. >>syms ep >>a=routh([1 1 2 2 3 5],ep) The above given case is for encountering a zero in the first column..

  • Platform: Matlab, Scripts

DIRECTORIES: - SMALLPART/ smallpart.m clusterindex.m - PARTITIONS/ partition.m cluster.m BLLSG.m Both are based on the Cluster Polynomial Representation of binary words of arbitrary length. The theory of Universal Lexicons is covered in the following Technical Report (submitted in J. App. Comp. Math.) http://cag.dat.demokritos.gr/publications/TR2011-1.pdf smallpart.m is a method for small combinatoric groups based on the internal MATLAB function ff2n for lexicon matrices It also uses a simpler function for cluster polynomial coefficients partition.m is based on a Sequential Lexicon Line Generator (a simple addition automaton) for words of arbitrary length (up to 2^32 for ordinary installations) The clusters.

  • Platform: Matlab, Scripts

LaguerreGen calculates the generalized Laguerre polynomial L{n, alpha} This function computes the generalized Laguerre polynomial L{n,alpha}. If no alpha is supplied, alpha is set to zero and this function calculates the "normal" Laguerre polynomial. Input: - n = nonnegative integer as degree level - alpha >= -1 real number (input is optional) The output is formated as a polynomial vector of degree (n+1) corresponding to MATLAB norms (that is the highest coefficient is the first element). Possible usage: - polyval(LaguerreGen(n, alpha), x) evaluates L{n, alpha}(x) - roots(LaguerreGen(n, alpha)) calculates roots of L{n, alpha} Calculation is done recursively using matrix operations for very fast execution time.

  • Platform: Matlab, Scripts

One function produces the Laguerre polynomial and the other integrates.

  • Platform: Matlab, Scripts

Polynomial division by convolution. Calculate inverse Z-transform -- (Polynomial division) - Up to K terms, q(z) = b(z)/a(z), where b(z)=b(0)+...+b(k)/z^k +...+b(n)/z^n. a(z)=a(0)+...+a(k)/z^k +...+a(m)/z^m. q(z)=q(0)+...+q(k)/z^k +...+q(K)/z^K + ...... If coefficients of b(x) and a(x) are all integers, then the entire process may involve integer arithmetric perations only. The round-off errors may therefore be eliminated. This code is similar to the code by Tamer Abdelazim Mellik's "Calculate inverse Z-transform by long division.".

  • Platform: Matlab, Scripts

It returns a vector POL, if it exists, such that conv(POL,POL) = P. P is a vector whose elements are the coefficients of a polynomial in descending powers.

  • Platform: Matlab, Scripts

For a given real-valued function of one real variable on an interval, the code calculates the best approximation in the uniform (max) norm by a polynomial of a given degree. Approximating in a uniform norm is much computationally harder compared to the standard least squares fit, but gives eye pleasing results. It can be viewed as an optimal polynomial interpolation, where the interpolating nodes are not known in advance, but rather determined by the algorithm. The polynomial that best approximates the data (X,Y) in the discrete uniform norm, i.e. the polynomial with the minimum value of max{ | p(x_i) - y_i | , x_i in X }, also known as min-max (or minimax) polynomial, is obtained by the exchange algorithm.

  • Platform: Matlab, Scripts

% Polynomial Interpolation Problem: Lagrange Form % x and y are vectors with the same dimensions % Given n points: (x_k,y_k) k = 1,2,...n % this function finds a polynomial P(x) of degree less % than n such that P(x_k) = y_k % -- % Remarks: % The resulting polynomial is displayed in symbolic notation % -- % Example % x=[0 1 2 3 4 5 6 7]; % y=[4 -6 -1 16 -2 6 12 17]; % pol=show_polinterp(x,y); % -- % x=[1 2 3 4 5 6 7]; % y=1+x.^3-x.^6; % pol=show_polinterp(x,y); % % For evaluating pol, try % subs(pol,x), it will return vector y %--.

  • Platform: Matlab, Scripts

This code implements the 1D polynomial regression method. It uses the least square method for the finding of regression polynomial coefficents. Outputs of the script are polynomial regression coefficients, residuals, the sum of squared errors, the determination index and the graphical comparison of the regression model and input data..

  • Publisher: Martin V
  • Date: 10-04-2013
  • Size: 10 KB
  • Platform: Matlab, Scripts

POLYFACT Polynomial Factorization Q = POLYFACT(A) returns the factorization of polynomial A. Input variable A must be a vector with integer coefficients in descending order. e.g. [3 7 2] represents 3*x^2+7x+2 Output Q is a cell array with each index being a polynomial factor, with integer coefficients in descending order. If polynomial A cannot be factored it will be returned unchanged as the output. As a sign convention, whenever possible the leading term for each polynomial factor will be positive. EXAMPLE: a=[-36 6 48 -21]; Q=polyfact(a) %Q{1} = [-3] %Q{2} = [2 -1] %Q{3} = [6 2 -7] a=[3 -3 1]; Q=polyfact(a) %Q{1} = [3 -3 1].

  • Platform: Matlab, Scripts

This interpolation package re-implements Matlab's built in methods ppval (1-d case polynomial evaluator) and ppual (multidimensional polynomial evaluator) which are used by Matlab to evaluate polynomial in their so called "pp-form". Matlab's built in versions are extrimely slow even though considering their high relative importance in many fields, such as finance or computer graphics. In my own field efficient polynomial evaluation is as important as efficient FFT is for signal processing engineers. This package introduces two functions named ppmval and ppuval ('m' for multivariate, 'u' for univariate) which evaluate general polynomials in their pp-form.

  • Platform: Matlab, Scripts

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