interpretation of ode solver stats

Hi,

I am using different solvers to solve a stiff ODE with a (non-constant) mass-matrix. The size of the system is about 70.

I am using the following options:

opt = odeset('Jacobian', @jacobian, 'Mass', @massmatrix, ...
             'MStateDependence', 'weak', ...
             'stats', 'on');

In the interest of potentially finding opportunities to improve performance, I am looking at the solver statistics.

Using ode15s, I get the following:

27930 successful steps

18568 failed attempts

83300 function evaluations

10844 partial derivatives

25440 LU decompositions

83299 solutions of linear systems

Using ode23t, I get the following:

12803 successful steps

12141 failed attempts

47784 function evaluations

6982 partial derivatives

17132 LU decompositions

47783 solutions of linear systems

ode23t seems more efficient for this problem.

Also, ode23t, for the same solver options such as default tolerance gives a better solution in terms of other problem-specific measures such as energy conservations etc. This is probably to be expected since the ode23t documentations says "... and you need a solution without numerical damping".

The following are my questions:

1. Why the number of LU decompositions is greater than the number of partial derivative (jacobian) evaluations? Is it because this count includes factorization of not only the jacobian, but also the mass matrix?
2. One option that can be supplied is 'MvPattern', which makes me think that the solvers are computing derivatives of the mass matrix. Is there a way to determine the count of such computations, and if there is room for improving efficiency there?
3. Is there any guidance to minimize the number of failed attempts?

Thank you.

Siva