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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Comparison study of series approximation and convergence between Chebyshev and Legendre series
TL;DR: Chebyshev and Legendre series have been widely used in many areas of physics and engineering as discussed by the authors, and they have been examined on the efficacy of both seris in terms of series approximation and convergence.
3
Designing nonlinearity characterization for mixed-signal circuits in system-on-chip
Byoungho Kim,Jacob A. Abraham +1 more
TL;DR: In this paper, a cost-effective self-test methodology was proposed to characterize the linearity performance of differential mixed-signal circuits in loopback mode. But, the proposed method is limited to single-ended MIMO circuits.
2
Machine-Efficient Chebyshev Approximation for Standard Statistical Distribution Functions
David Lester,Mohammed A. Abutheraa +1 more
- 01 Jan 2008
TL;DR: This paper extends the idea of Brisebarre, Muller, Tisserand, and Chevillard on machine-efficient Chebyshev approximation to standard statistical distribution functions, by which they mean: the normal distribution, the beta distribution,The F-distribution, and the Student’s t-dist distribution.
1
Direction of Arrival Estimation for Nonuniform Planar Array Based on Piecewise Interpolation Method
TL;DR: In this paper, the problem of direction-of-arrival (DOA) estimation by using spectral search for a non-uniform planar array is addressed by dividing the MUSIC null-spectrum function into a number of equal subintervals.
Polynomially knotted 2-spheres
Rama Shanker. Mishra
- 14 Jul 2023
TL;DR: In this paper , it was shown that every proper, smooth 2-knot is ambient isotopic to a polynomial embedding from Ω( √ n) to √ log n, where n is the number of knots in the graph.
References
•Book
Numerical Analysis: Mathematics of Scientific Computing
David R. Kincaid,Ward Cheney +1 more
- 14 Jan 1991
TL;DR: This work treats numerical analysis from a mathematical point of view, demonstrating that the many computational algorithms and intriguing questions of computer science arise from theorems and proofs.
1.2K
•Book
Computability in analysis and physics
Marian Boykan Pour-El,J. Ian Richards +1 more
- 01 Jan 1989
TL;DR: This book represents the first treatment of computable analysis at the graduate level within the tradition of classical mathematical reasoning and is sufficiently detailed to provide an introduction to research in this area.
1K
•Book
Elementary Functions: Algorithms and Implementation
Jean-Michel Muller
- 15 Jul 1997
TL;DR: I found the book well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find.
676
•Book
Complexity theory of real functions
Ker-I Ko
- 01 Jan 1991
TL;DR: " polynomial complexity theory extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems.
645