In this paper, the origins of spurious solutions occurring in the high-order finite difference methods are studied. Based on a uniform mesh, spurious modes are found in the high-order one-sided finite difference discretizations of many eigenvalue problems. Spurious modes are classified as spectral pollution and non-spectral pollution. The latter can be partially avoided by mesh refinement, whil...

In the Hopfield model of content addressable memory, the number of spurious attractors is exponential in the dimensionality of the memory. Hence it is highly ’ikely that the system converges to a spurious memory on ar arbitrary input. It is desirable that the system has a way c:f checking whether its state corresponds to any one of the stored patterns. In this paper we show that it is possible ...

Supercell models are often used to calculate the electronic structure of local perturbations from ideal periodicity in bulk or on surface a crystal wires. When defect adsorbent is charged, jellium counter charge applied maintain overall neutrality, but interaction artificially repeated charges has be corrected, both total energy and one-electron eigenvalues eigenstates. This becomes paramount s...

Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

This dissertation offers a new cluster detection method. This method looks at the cluster detection problem from a new perspective. I change the question of “What do real clusters look like?” to the question of “What do spurious clusters look like?” and “How do spurious clusters affect the ability to recover real clusters?” Spurious clusters can be identified from their geographical characteris...