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.
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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.
5
References
•Book
Chebyshev polynomials : from approximation theory to algebra and number theory
Theodore J. Rivlin
- 01 Jun 1990
TL;DR: The Chebyshev Polynomials as mentioned in this paper have some elementary and extreme properties, such as extension of functions, iterative properties, and number-theoretic properties, including algebraic properties.
567
On the computational complexity of best Chebyshev approximations
TL;DR: On the basis of a formal model of computation, it is shown that the question of whether the best Chebyshev approximations of polynomial-time computable functions on [0, 1] are always polynomially computable depends on the relationship among well-known discrete complexity classes.
18
•Book
Calculus With Analytic Geometry
Earl William Swokowski
- 01 Jun 1968
TL;DR: The mathematics in this chapter will be review for you however the examples will be oriented toward applications and so will take some thought in the x y coordinate system.