  We present a new algorithm which is named the Dynamical Functional Particle
Method, DFPM. It is based on the idea of formulating a finite dimensional
damped dynamical system whose stationary points are the solution to the
original equations. The resulting Hamiltonian dynamical system makes it
possible to apply efficient symplectic integrators. Other attractive properties
of DFPM are that it has an exponential convergence rate, automatically includes
a sparse formulation and in many cases can solve nonlinear problems without any
special treatment. We study the convergence and convergence rate of DFPM. It is
shown that for the discretized symmetric eigenvalue problems the computational
complexity is given by $\mathcal{O}(N^{(d+1)/{d}})$, where \emph{d} is the
dimension of the problem and \emph{N} is the vector size. An illustrative
example of this is made for the 2-dimensional Schr\"odinger equation.
Comparisons are made with the standard numerical libraries ARPACK and LAPACK.
The conjugated gradient method and shifted power method are tested as well. It
is concluded that DFPM is both versatile and efficient.
