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\title{Quadratic programming methods for positive solutions of 
ill-conditioned linear inverse problems with constrained 
singular-function coefficients.}  
\author{E R Pike\\
Physics Department, King's College, London, UK}
\date{}
\maketitle
The study of Fredholm equations of the first kind, which are
ill-posed inverse problems, is an area of physics and
mathematics that is currently flourishing, with applications 
in many practical areas of interest, ranging from the restoration 
of diffraction-limited optical images to problems in high-
temperature superconductivity. Problems of this type are 
characterised by a forward relation that includes some loss 
of information which makes calculating the backward
relation impossible without additional constraints on the 
solution.  Work is presented which attempts to add in some of 
this lost information by making use of such constraints as
positivity or known moments while preserving the coefficients
of low-order singular-functions, which are accurately inverted.
This is achieved by the method of quadratic programming, with 
a choice of optimisation criteria including minimum global L(1) 
and L(2) norm solutions. The results are salutory.
\end{document}

E.R. Pike
