@TechReport{	  it:2003-054,
  author	= {Martin Nilsson},
  title		= {Stability of the Fast Multipole Method for {H}elmholtz
		  Equation in Three Dimensions},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2003},
  number	= {2003-054},
  month		= nov,
  abstract	= {Stability limits for the diagonal forms approximating the
		  free space Green's function in Helmholtz' equation are
		  derived. It is shown that while the original approximation
		  of the Green's function is stable except for overflows, the
		  diagonalized form becomes unstable due to errors from
		  roundoff, interpolation, choice of quadrature rule and
		  approximation of the translation operator. Numerical
		  experiments validate the theoretical estimates.}
}