The discrete analogue of Laplace's method

A Discrete Collocation Method for Boundary Integral Equations

We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...

Application of Discrete Laplace's Equation to Create Topography Map of Near-infrared Spectroscopy Signal

Near-infrared spectroscopy (NIRS) enables non-invasive measurement of hemoglobin concentration changes in the cerebral cortex. Creation of a topography map is an important evaluation method used in clinical NIRS studies. In this study, we used Laplace's equation method to create topography maps of NIRS. The method was tested and found to converge very precisely. The method was applied to NIRS s...

Discrete analogues of Laplace's approximation

Logarithmic Convexity for Discrete Harmonic Functions and the Approximation of the Cauchy Problem for Poisson's Equation

Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard C" piecewise-linear approximation to Laplace's equation are proved. Using this result, error estimates for a regularizaron method for approximating the Cauchy problem for Poisson's equation on a rectangle are obtained. Numerical results are presented.

Laplace's Method Approximations for Probabilistic Inference in Belief Networks with Continuous Variables

Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with continuous variables. This technique approximates posterior moments and marginal posterior distributions with reasonable accuracy [errors are O(n ) for posterior mea...