Applying Computer Algebra Systems in Approximating the Trigonometric Functions
| Autor: | Thái Anh Nhan, Le Phuong Quan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Current (mathematics)
pointwise approximate polynomial Computer science 02 engineering and technology engineering.material lcsh:QA75.5-76.95 symbols.namesake ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0202 electrical engineering electronic engineering information engineering Taylor series Trigonometric functions Point (geometry) Sine approximation Maple Applied Mathematics lcsh:T57-57.97 lcsh:Mathematics 020208 electrical & electronic engineering General Engineering approximate value Symbolic computation lcsh:QA1-939 020202 computer hardware & architecture Numerical integration Algebra Computational Mathematics Taylor polynomial lcsh:Applied mathematics. Quantitative methods engineering symbols piecewise approximate polynomial lcsh:Electronic computers. Computer science |
| Zdroj: | Mathematical and Computational Applications, Vol 23, Iss 3, p 37 (2018) Mathematical and Computational Applications Volume 23 Issue 3 |
| ISSN: | 2297-8747 |
| Popis: | We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor’s expansion about a point having a form of k p , k ∈ Z and p = π / 2 , and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximating π with a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the use of algorithms. Numerical and graphical results are implemented by MAPLE. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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