Abstract
Matrices generated by finite elements usually have high condition numbers which may spoil the accuracy of their lowest eigenvalues. This chapter considers some common classes of such matrices. These matrices are determined by some parameters which are not merely their non-zero elements. These parameters determine well the eigenvalues and the eigenvectors and the Cholesky factor. The latter is shown to be a perfect condition estimator and rank revealer. Though accurate computation of this factor is still an open problem, success has been achieved to perform it only for some very simple cases: the simple chain and the simple loop with an arbitrary number of earth connections.
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