Improving the stability of a discrete least-squares method for membrane eigenvalue problems
نویسنده
چکیده
In this article it is shown how to improve the numerical stability of a discrete least-squares method for computing eigenvalue approximations of the Laplace operator defined on standard two-dimensional domains. Among many sets of matching points the smallest condition numbers of the corresponding matrices have been obtained by using the Morrow-Patterson and Padua points in the square case, the Fekete points in the triangular case, and the Chebyshev disc points for the unit disc. The approximations of the first few vibration frequencies of a nonhomogeneous square membrane, and homogeneous circular and triangular membranes are presented.
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