Convergence of numerical differentiation

Numerical Methods 101 - Convergence of Numerical Models

Verifying Numerical Convergence Rates

2 Determining the order of accuracy We are often faced with the problem of how to determine the order p given a sequence of approximations ũh1 , ũh2 , . . . This is can be a good check that a method is correctly implemented (if p is known) and also a way to get a feeling for the credibility of an approximation ũh (high p means high credibility). We can either be in the situation that the exact ...

Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints I: Convergence Results for Backward Differentiation Formulas

In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in the modelling of problems from physics and engineering; we study some particular examples from electrical networks, fluid dynamics and constrained mechanical systems. We show that backward differenti...

On stable numerical differentiation

A new approach to the construction of finite-difference methods is presented. It is shown how the multi-point differentiators can generate regularizing algorithms with a stepsize h being a regularization parameter. The explicitly computable estimation constants are given. Also an iteratively regularized scheme for solving the numerical differentiation problem in the form of Volterra integral eq...

Asymptotic Convergence of Backpropagation: Numerical Experiments

Yu He Dept. of Physics Ohio State Univ. Columbus, OH 43212 We have calculated, both analytically and in simulations, the rate of convergence at long times in the backpropagation learning algorithm for networks with and without hidden units. Our basic finding for units using the standard sigmoid transfer function is lit convergence of the error for large t, with at most logarithmic corrections f...