Fast Algorithm For Evaluation Research Articles

Recursive algorithm for fast evaluation of the Abel inversion integral in broadband reflectometry

The application of Kalman filtering is proposed for the numerical evaluation of plasma density profiles using noisy group delay data obtained from O-mode frequency-modulated broadband reflectometry. This method allows faster computation of the Abel inversion integral than the usual numerical methods (e.g., the trapezoidal rule) while maintaining a good accuracy in the presence of noise. In addition, density profiles with different degrees of smoothing can be produced by adjusting a single parameter. The algorithm seems promising in applications to plasma control in real time.

Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters

In computer simulations of molecular conformation and protein folding, a significant part of computing time is spent in the evaluation of potential energy functions and force fields. Therefore many algorithms for fast evaluation of potential energy functions and force fields are proposed in the literature. However, most of these algorithms assume that the particles are uniformly distributed in order to guarantee good performance. In this paper, we prove that the minimum inter-particle distance at any global minimizer of Lennard-Jones clusters is bounded away from zero by a positive constant which is independent of the number of particles. As a by-product, we also prove that the global minimum of an n particle Lennard-Jones cluster is bounded between two linear functions. Our first result is useful in the design of fast algorithms for potential function and force field evaluation. Our second result can be used to decide how good a local minimizer is.

Fast evaluation of R�dei functions

We introduce a fast evaluation algorithm for Redei functions of complexityO(log2n). Redei functions are of interest in cryptographic applications and primality testing.

Fast discrete Fourier transform with exponentially spaced points

The use of fast algorithms for evaluation of discrete Fourier transform-inverse transform pairs with uniformly spaced input data but with output data required only at exponentially spaced intervals is investigated. The algorithms require order (N) arithmetic operations, rather than the order (N log(N)) required for the full FFT algorithm.

A Fast Algorithm to Solve the Beltrami Equation with Applications to Quasiconformal Mappings

Two algorithms are provided for the fast and accurate computation of the solution of Beltrami equations in the complex plane in the interior of a unit disk. There are two integral operators which are fundamental in the construction of this solution. A fast algorithm to evaluate one of these integrals is given by Daripa (SIAM J. Sci. Stat. Comput., Nov. 1992). An algorithm for fast evaluation of the second integral is provided here. These algorithms are based on representation of the solution in terms of a double integral, some recursive relations in Fourier space, and fast Fourier transforms. The theoretical computational complexity of our algorithm isO(MN InN), whereM andN are the number of nodes in the circular and radial directions. We show the application of these algorithms in constructing numerical methods for quasiconformal mappings. A numerical method is provided and explored numerically for the construction of quasiconformal mappings using the Beltrami equation. In particular we show the effect of dilatations on the Jacobian of the mappings which controls what is known as the crowding phenomenon in the literature.

A fast algorithm to solve the Beltrami equation with applications to quasiconformal mappings

Two algorithms are provided for the fast and accurate computation of the solution of Beltrami equations in the complex plane in the interior of a unit disk. There are two integral operators which are fundamental in the construction of this solution. A fast algorithm to evaluate one of these integrals is given by Daripa ( SIAM J. Sci. Stat. Comput., Nov. 1992). An algorithm for fast evaluation of the second integral is provided here. These algorithms are based on representation of the solution in terms of a double integral, some recursive relations in Fourier space, and fast Fourier transforms. The theoretical computational complexity of our algorithm is O( MN In N), where M and N are the number of nodes in the circular and radial directions. We show the application of these algorithms in constructing numerical methods for quasiconformal mappings. A numerical method is provided and explored numerically for the construction of quasiconformal mappings using the Beltrami equation. In particular we show the effect of dilatations on the Jacobian of the mappings which controls what is known as the crowding phenomenon in the literature.

Comments on "An Algorithm for Fast Evaluation of Time Functions"

Comments on "An Algorithm for Fast Evaluation of Time Functions"

Algorithms for fast evaluation of Boolean expressions

For Boolean functions whose variables appear in secondary storage, algorithms which minimize the expected cost of evaluation are considered. An easyto-implement algorithm which gives nearly optimal results is proposed for the case of monotonic functions without a priori probabilities. Optimality proofs are given for a simple special cases.