@TechReport{	  it:2010-029,
  author	= {Owe Axelsson and Maya Neytcheva},
  title		= {A General Approach to Analyse Preconditioners for
		  Two-by-Two Block Matrices},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2010},
  number	= {2010-029},
  month		= nov,
  abstract	= {Two-by-two block matrices arise in various applications,
		  such as in domain decomposition methods or, more generally,
		  when solving boundary value problems discretized by finite
		  elements from the separation of the node set of the mesh
		  into 'fine' and 'coarse' nodes. Matrices with such a
		  structure, in saddle point form arise also in mixed
		  variable finite element methods and in constrained
		  optimization problems.
		  
		  A general algebraic approach to construct, analyse and
		  control the accuracy of preconditioners for matrices in
		  two-by-two block form is presented. This includes both
		  symmetric and nonsymmetric matrices, as well as indefinite
		  matrices. The action of the preconditioners can involve
		  element-by-element approximations and/or geometric or
		  algebraic multigrid/multilevel methods.}
}