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Empowering Human Decision-Making in AI Models: The Path to Trust and Transparency
Open Access
ARTICLE
CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 281-312, 2009, DOI:10.3970/cmes.2009.044.281
Abstract Here we develop a general purpose pre/post conditionerT, to solve an ill-posed system of linear equations,Ax=b. The conditionerTis obtained in the course of the solution of the Laplace equation, through a boundary-collocation Trefftz method, leading to:Ty=x, whereyis the vector of coefficients in the Trefftz expansion, andxis the boundary data at the discrete points on a unit circle. We show that the quality of the conditionerTis greatly enhanced by using multiple characteristic lengths (Multiple Length Scales) in the Trefftz expansion. We further show thatTcan be multiplicatively decomposed into a dilationTDand a rotationTR. For an odd-orderedA, we develop four conditioners based on… More >
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