Taylor Model

In CORA, Taylor models are instantiated by

% tay = taylm(I,max_order,name);

where I is the interval domain, max_order is the maximum polynomial order and name is the name of the variable.

Example:

% initialize Taylor model

tx = taylm(interval(-2,2),4,'x');

tay = [tx; sin(tx)];

% plot Taylor model

plot(tay);

For more information, type

help taylm
  taylm (Taylor model) class.
 
  Syntax:
     obj = taylm(int)
     obj = taylm(int,max_order,names,opt_method,eps,tolerance)
     obj = taylm(func,int)
     obj = taylm(func,int,max_order,opt_method,eps,tolerance)
 
  Inputs:
     int - interval object that defines the ranges of the variables
     max_order - the maximal order of a polynomial stored in a polynomial part
     names - cell-array containing the names of the symbolic variables as
             characters (same size as interval matrix 'int')
     func - symbolic function 
     opt_method - method used to calculate interval over-approximations of
                  taylor models 
                   'int': standard interval arithmetic (default)
                   'bnb': branch and bound method is used to find min/max
                   'bnbAdv': branch and bound with re-expansion of taylor models
                   'linQuad': optimization with Linear Dominated Bounder (LDB)
                              and Quadratic Fast Bounder (QFB)
     eps - precision for the selected optimization method (opt_method = 'bnb', 
           opt_method = 'bnbAdv' and opt_method = 'linQuad')
     tolerance - monomials with coefficients smaller than this value are
                 moved to the remainder
 
  Outputs:
     obj - generated object
 
  Examples: 
     % create and manipulate simple taylor models
     tx = taylm(interval(1,2),4,'x');
     ty = taylm(interval(3,4),4,'y');
     t = sin(tx+ty) + exp(-tx) + ty*tx;
     interval(t)
 
     % create a vector of taylor models
     tvec = taylm(interval([1;3],[2;4]),4,{'x';'y'});
     t = sin(tvec(1)+tvec(2)) + exp(-tvec(1)) + tvec(1)*tvec(2);
     interval(t)
 
     % create a taylor model from a symbolic function
     syms x y
     func = sin(x+y) + exp(-x) + x*y;
     t = taylm(func,interval([1;3],[2;4]),4);
     interval(t)
 
  Other m-files required: none
  Subfunctions: none
  MAT-files required: none
 
  See also: interval
 
  References: 
    [1] K. Makino et al. "Taylor Models and other validated functional 
        inclusion methods"
    [2] M. Althoff et al. "Implementation of Taylor models in CORA 2018
        (Tool Presentation)"

    Documentation for taylm
    Other uses of taylm
    Folders named taylm