Navegando por Autor "Biezuner, Rodney Josué"

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Computing the first eigenvalue of the p-Laplacian via the inverse power method.
(2009) Biezuner, Rodney Josué; Ercole, Grey; Martins, Eder Marinho
In this paper, we discuss a new method for computing the first Dirichlet eigenvalue of the p-Laplacian inspired by the inverse power method in finite dimensional linear algebra. The iterative technique is independent of the particular method used in solving the p-Laplacian equation and therefore can be made as efficient as the latter. The method is validated theoretically for any ball in Rn if p >1 and for any bounded domain in the particular case p = 2. For p >2 the method is validated numerically for the square.
Computing the sinP Function via the inverse power method.
(2010) Biezuner, Rodney Josué; Ercole, Grey; Martins, Eder Marinho
In this paper, we discuss a new iterative method for computing sinp. This function was introduced by Lindqvist in connection with the unidimensional nonlinear Dirichlet eigenvalue problem for the p-Laplacian. The iterative technique was inspired by the inverse power method in finite dimensional linear algebra and is competitive with other methods available in the literature.
Eigenvalues and eigenfunctions of the Laplacian via inverse iteration with shift.
(2012) Biezuner, Rodney Josué; Ercole, Grey; Giacchini, Breno Loureiro; Martins, Eder Marinho
In this paper we present an iterative method, inspired by the inverse iteration with shift technique of finite linear algebra, designed to find the eigenvalues and eigenfunctions of the Laplacian with homogeneous Dirichlet boundary condition for arbitrary bounded domains X _ RN. This method, which has a direct functional analysis approach, does not approximate the eigenvalues of the Laplacian as those of a finite linear operator. It is based on the uniform convergence away from nodal surfaces and can produce a simple and fast algorithm for computing the eigenvalues with minimal computational requirements, instead of using the ubiquitous Rayleigh quotient of finite linear algebra. Also, an alternative expression for the Rayleigh quotient in the associated infinite dimensional Sobolev space which avoids the integration of gradients is introduced and shown to be more efficient. The method can also be used in order to produce the spectral decomposition of any given function u 2 L2ðXÞ.