Integration-free interval doubling for Riccati equation solutions

Various algorithms are given for the case of constant coefficients. The algorithms are based on two ideas: first, relate the Re solution with general initial conditions to anchored RE solutions; and second, when the coefficients are constant the anchored solutions have a basic shift-invariance property. These ideas are used to construct an integration free superlinearly convergent iterative solution to the algebraic RE. The algorithm, arranged in square-root form, is thought to be numerically stable and competitive with other methods of solving the algebraic RE

Gaussian integration with rescaling of abscissas and weights

An algorithm for integration of polynomial functions with variable weight is considered. It provides extension of the Gaussian integration, with appropriate scaling of the abscissas and weights. Method is a good alternative to usually adopted interval splitting.Comment: 14 pages, 5 figure

ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a particular solution defined on each sub-interval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time-domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique.Comment: Corrected typos. arXiv admin note: text overlap with arXiv:1607.0036

Television noise-reduction device

System greatly improves signal-to-noise ratio with little or no loss in picture resolution. By storage of luminance component, which is summed with chrominance component, system performs mathematical integration of basically-repetitive television signals. Integration of signals over interval of their repetition causes little change in original signals and eliminates random noise

A study to determine the usefulness of interval analysis in solving problems in celestial mechanics

This investigation was undertaken to determine the usefulness of interval analysis to numerical integration and matrix inversion techniques and to combine these results to determine the value of interval analysis in bounding computational errors in the two-body problem. Conclusions were that interval analysis may be worthwhile in certain small scale isolated problems, but its usefulness in any large scale problem is doubtful

Effects of integration time on in-water radiometric profiles

This work investigates the effects of integration time on in-water downward irradiance E-d, upward irradiance E-u and upwelling radiance L-u profile data acquired with free-fall hyperspectral systems. Analyzed quantities are the subsurface value and the diffuse attenuation coefficient derived by applying linear and non-linear regression schemes. Case studies include oligotrophic waters (Case-1), as well as waters dominated by colored dissolved organic matter (CDOM) and non-algal particles (NAP). Assuming a 24-bit digitization, measurements resulting from the accumulation of photons over integration times varying between 8 and 2048ms are evaluated at depths corresponding to: 1) the beginning of each integration interval (FST); 2) the end of each integration interval (LST); 3) the averages of FST and LST values (AVG); and finally 4) the values weighted accounting for the diffuse attenuation coefficient of water (WGT). Statistical figures show that the effects of integration time can bias results well above 5% as a function of the depth definition. Results indicate the validity of the WGT depth definition and the fair applicability of the AVG one. Instead, both the FST and LST depths should not be adopted since they may introduce pronounced biases in E-u and L-u regression products for highly absorbing waters. Finally, the study reconfirms the relevance of combining multiple radiometric casts into a single profile to increase precision of regression products. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement