Tagged Questions
2
votes
3answers
41 views
Series evaluated to $m$ terms, approximating the error
Given a series $\displaystyle\sum_{n=0}^\infty a_n$, how can we bound the error (which I shall denote with $R_n$) when we evaluate it to $m$ terms?
$$\sum_{n=0}^\infty a_n \approx \sum_{n=0}^m a_n$$
...
1
vote
0answers
17 views
Is there a way to estimate the range of fitting coefficients from only the data?
Considering an approximation $f$ for a set of $N$ data points $(x,y)$ using, for example, $M$ radial basis functions at arbitrary sites in the domain
$f_i = \sum_{j=1} ^M c_j\phi(||x_i-x_j||)$
where ...
2
votes
3answers
60 views
Precision with Taylor Expansions
when you take a 1st order taylor expansion of a function, so:
$$f(a) + f'(a)(x-a)$$
does that mean that if the result is only accurate to one decimal place?
so for a value a.bcd, d would be the ...
3
votes
2answers
348 views
Modern formula for calculating Riemann Zeta Function [duplicate]
Possible Duplicate:
How to evaluate Riemann Zeta function
I have an amateur interest in the Zeta Function. I have read Edward's book on the topic, which is perhaps a little dated. I would ...
1
vote
2answers
242 views
Help with Chebyshev Economization of $\exp(x)$?
This may be a stupid question, so I apologize in advance if it is. This is a very common example of Chebyshev Economization, but I still do not understand how the coefficients are found. I want to ...
3
votes
0answers
74 views
Numerically estimate $a^b$ [duplicate]
Possible Duplicate:
How can I calculate non-integer exponents?
What is the most efficient way to estimate $a^b$ ($a > 0$) numerically?
My goal is not to use built-in math functions (like ...
2
votes
1answer
126 views
Best and most efficient way to numerically compute $e$?
There are many well-known methods for efficiently numerically computing $\pi$, such as Chudnovsky's Method or perhaps Gauss-Legendre's algorithm.
I was wondering what the best method for computing $e$ ...
2
votes
1answer
304 views
Method for estimating the nth derivative?
When using numerical analysis, I often find that I am required to estimate a derivative (e.g. when using Newton Iteration for finding roots). To estimate the first derivative of a function $f(x)$ at ...
