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Linearity is exploited by formulating the boundary value problem (BVP) solution in terms of Green’s functions (GFs) which may be precomputed to provide speed and cheap lookup operations.

Runtime BVPs are solved using a collection of Capacitance Matrix Algorithms (CMAs) based on the Sherman-Morrison-Woodbury formula.

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We show that leave-one-out cross-validation of kernel Fisher discriminant classifiers can be implemented with a computational complexity of only O(l³) operations rather than the O(l^4) of a nave implementation, where l is the number of training patterns.

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It appears in MATLAB 7.2 as x=A\b when A is sparse symmetric positive definite, as well as in several other sparse matrix functions. We show that leave-one-out cross-validation of kernel Fisher discriminant classifiers c ..." Mika et al.

[1] apply the "kernel trick" to obtain a non-linear variant of Fisher's linear discriminant analysis method, demonstrating state-of-the-art performance on a range of benchmark datasets.

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