Abstract:
	We investigate existing and novel methods to approximate matrix functions
	using subspace methods. A two-sided harmonic Ritz approach is analyzed and
	applied to the extraction from a subspace for matrix functions.
	We derive all methods in various ways and provide a framework to fit in the
	techniques.

Keywords:
	Matrix function, matrix exponential, Ritz values, harmonic Ritz values,
	two-sided Ritz values, two-sided harmonic Ritz values, Petrov values,
	harmonic Petrov values, interpolation, Dunford-Taylor integral.

AMS:
	65F10, 65F50, 65A99, 65A20.