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
Chebyshev expansion for accurate and efficient 2D PSP bistatic point target spectrum
Carmine Clemente,John J. Soraghan +1 more
- 01 Jan 2012
TL;DR: This paper presents a modified bistatic point target spectrum based on the 2 dimensional principle of stationary phase with the accuracy improved by the use of a Chebyshev polynomial approximation to provide a more accurate approximation reducing the phase error.
Machine-efficient Chebyshev approximation for exact arithmetic: their use with first-order ordinary differential equations
Mohammed A. Abutheraa,David Lester +1 more
- 11 Apr 2010
TL;DR: It is demonstrated that these machine-efficient Chebyshev approximations do indeed improve the efficiency with which these operations can be performed.
High-Accuracy Machine-Efficient Chebyshev Approximation: an Application to Spectral Methods for Sobolev Spaces
Mohammed A. Abutheraa,David Lester +1 more
- 12 Aug 2009
TL;DR: Experimental evaluation demonstrates that machine efficient approximations do indeed improve the efficiency with which these operations can be performed and has an application to spectral methods for sobolev spaces.
Phương pháp số ước lượng hàm truyền biểu diễn độ dịch chuyển của thiết bị ngầm được lai dắt bằng cáp dưới tác động của sóng biển
Vu Duc Tuan Tuấn,Nguyen Phu Dang +1 more
TL;DR: Phương pháp số ước lượng TF của TUV bằng mô hình gần đúng với sai số yêu cầu dựa trên phương pháp nội suy thực.
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