Open AccessJournal Article
Computable Function Representations Using Effective Chebyshev Polynomial
TL;DR: The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.
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Abstract: We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.
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Citations
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Parameterized Uniform Complexity in Numerics: from Smooth to Analytic, from NP-hard to Polytime
TL;DR: It turns out that Gevrey's hierarchy of functions climbing from analytic to smooth corresponds to the computational complexity of maximization growing from polytime to NP-hard.
18
Approximation of the Bistatic Slant Range Using Chebyshev Polynomials
TL;DR: A new Chebyshev slant range function approximation is presented that is shown to increase the accuracy of the analytical approximation of the bistatic point target spectrum and yield a more accurate spectrum that can be exploited in bistatics SAR focusing algorithms.
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On the numerical solution of the integro-differential equation of the point kinetics of nuclear reactors
TL;DR: In this article, the integro-differential equation of the point kinetics of nuclear reactor was solved by approximating the neutron density with piecewise polynomial and exponential functions.
11
Stability of narrow-gap Taylor-Dean flow with radial heating: Stationary critical modes
Rudra Kanta Deka,Ashish Paul +1 more
TL;DR: In this paper, a linear stability analysis for the Taylor-Dean flow, a viscous flow between concentric horizontal cylinders with a constant azimuthal pressure gradient, keeping the cylinders at different temperatures, when the inner cylinder is rotating and outer one is stationary has been implemented under the assumption that the gap spacing between the cylinders is small compared to the mean radius.
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Software Effort Estimation Using Functional Link Neural Networks Tuned with Active Learning and Optimized with Particle Swarm Optimization
Tirimula Rao Benala,Rajib Mall,Satchidananda Dehuri,Pala Swetha +3 more
- 18 Dec 2014
TL;DR: The computational results show that the active learning along with PSO optimized FLANN greatly improves the performance of the model and its variants for software development effort estimation.
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References
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Calculus with Analytic Geometry
Thurman Stewart Peterson
- 01 Jan 1936
TL;DR: In this article, the authors introduce a calculus of transcendental functions, and apply it to the Vector Calculus of Transcendental Functions (VCFL) and the Integral Calculus.
Computing machine-efficient polynomial approximations
TL;DR: This paper provides a general and efficient method for finding the best polynomial approximation under this constraint and also applies if some other constraints (such as requiring some coefficients to be equal to some predefined constants or minimizing relative error instead of absolute error) are required.
•Book
Numerical Analysis
J. Douglas Faires
- 01 Jan 1978
TL;DR: This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis, and describes the accuracy, efficiency and robustness of these algorithms.