Topic 10.6: Müller's Method (Matlab)

Introduction Notes Theory HOWTO Examples Engineering Error Questions Matlab Maple

Implementing Müller's method in Matlab is not that difficult:

eps_step = 1e-5;
eps_abs = 1e-5;
p = [1 2 3 4 2];
x = [0 -0.1 -0.2]';
y = polyval( p, x );
while ( true )
     V = vander( x - x(2) );
     c = V \ y;
     disc = sqrt( c(2)^2 - 4*c(1)*c(3) );

     % if ( real(c(2))*real(disc) + imag(c(2))*imag(disc) > 0 )

     if abs( c(2) + disc ) > abs( c(2) - disc )
         denom = c(2) + disc;
     else
         denom = c(2) - disc;
     end

     [roots(c)', -2*c(3)/denom, x'];

     x = [x(2), x(3), x(2) - 2*c(3)/denom]';

     y = [y(2), y(3), polyval( p, x(3) )]';

     if ( abs( x(2) - x(3) ) < eps_step && abs( y(3) ) < eps_abs )
        break;
     end
end
x(3)