Chebyshev
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A simple python module for approximating any sympy expression using the Taylor series and Chebyshev polynomials.
Chebyshev 
Introduction
A simple python module for approximating any sympy expression
using the Taylor series and Chebyshev polynomials.
It was created as a project for the DisCont mathematics 2 course at the Faculty of Electrical Engineering and Computing, University of Zagreb.
Installation
Requires at least python 3.6.
pip install -r requirements.txt
Submodules
The functionality is divided into two submodules:
chebyshev.polynomialwhich is used for computing and storing Chebyshev polynomials, as well as some other simple polynomial manipulation.chebyshev.approximationwhich is used for approximating anysympyexpression using the Taylor series and Chebyshev polynomials.
Approximated Functions
exp(x)log(x + 1)sin(x)/xcos(x)
exp(x)
Coefficients for exp(x) on the [0, 1] interval:
| Coefficient | Term |
|---|---|
+0.00228989065375017828 |
x6 |
+0.00686967196125053310 |
x5 |
+0.04293544975781583839 |
x4 |
+0.16601707239688789919 |
x3 |
+0.50019798967855455540 |
x2 |
+0.99996662485953080601 |
x |
+1.00000240440099563700 |
1 |
Maximum error on that interval is 2.724750259197606e-06
_approximation.png)
_absolute_error.png)
log(x + 1)
Coefficients for log(x + 1) on the [0, 1] interval:
| Coefficient | Term |
|---|---|
-1.78206380208333333330 |
x6 |
+1.68432617187500000000 |
x5 |
+1.23596191406250000000 |
x4 |
-0.76288859049479166667 |
x3 |
-0.86048889160156250000 |
x2 |
+1.16706848144531250000 |
x |
+0.01269240000891307044 |
1 |
Maximum error on that interval is 0.026814743150641585
_approximation.png)
_absolute_error.png)
sin(x)/x
Coefficients for sin(x)/x on the [-1, 1] interval:
| Coefficient | Term |
|---|---|
+0.00000269375975765659 |
x8 |
-0.00019835866408658445 |
x6 |
+0.00833331406945632250 |
x4 |
-0.16666666426123592319 |
x2 |
+0.99999999995192540491 |
1 |
Maximum error on that interval is 4.807454434541114e-11
_x_approximation.png)
_x_absolute_error.png)
cos(x)
Coefficients for cos(x) on the [-1, 1] interval:
| Coefficient | Term |
|---|---|
+0.00002412120108317053 |
x8 |
-0.00138829603431854838 |
x6 |
+0.04166645537534185744 |
x4 |
-0.49999997362171781040 |
x2 |
+0.99999999947287565593 |
1 |
Maximum error on that interval is 5.271243441740125e-10
_approximation.png)
_absolute_error.png)
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