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## polyvalm.m

 From: Ross A. Lippert Subject: polyvalm.m Date: Thu, 02 Dec 1999 11:31:46 -0700

```Here is a replacement for polyvalm.m which will give correct
answers for matrices which are non-diagonalizable.

The current version of polyvalm.m assumes the matrix has a
trivial eigenstructure.

-r

P.S. the file was produced by consulting polyvalm.m and polyval.m
and nothing else.```
```## usage: polyvalm (c, x)
##
## Evaluate a polynomial in the matrix sense.
##
## In octave, a polynomial is represented by it's coefficients (arranged
## in descending order). For example a vector c of length n+1 corresponds
## to the following nth order polynomial
##
##   p(x) = c(1) x^n + ... + c(n) x + c(n+1).
##
## polyvalm(c,X) will evaluate the polynomial in the matrix sense, i.e. matrix
## multiplication is used instead of element by element multiplication as is
## used in polyval.
##
## X must be a square matrix.
##
## SEE ALSO: polyval, poly, roots, conv, deconv, residue, filter,
##           polyderiv, polyinteg

## Author: Tony Richardson <address@hidden>
## Created: June 1994
## Adapted-By: jwe
## Changed-By: Ross Lippert <address@hidden,sandia.gov>

function y = polyvalm (c, x)

if (nargin != 2)
usage ("polyvalm (c, x)");
endif

if (! (is_vector (c) || isempty (c)))
error ("polyvalm: first argument must be a vector.");
endif

if (! is_square (x))
error("polyvalm: second argument must be a square matrix.");
endif

if (isempty (c))
y = [];
return;
endif

n = length(c);
I = eye(rows(x),columns(x));
y = c(1) * I
for index = 2:n,
y = c(index)*I + x*y;
endfor

if (is_symmetric (x))
y = (y+y')/2;
endif

endfunction
```

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