0
votes
0answers
24 views

Estimating the mean internal distance between borders of an irregular shape

I have two overlapping (not matching) irregular shapes ($X$ and $Y$), and I would like to estimate the mean distance between their limits. What I've been trying so far is obtaining the irregular ...
16
votes
3answers
268 views

Approximating $100!$

I participated in an Estimathon (a speed contest of Fermi problems) not long ago. It works as follows. Contestants are given questions and they must give a closed range $[a,b]$ which should contain ...
3
votes
1answer
59 views

Error of apprximation

Have anyone read book "Paul Glasserman Monte Carlo MIFE", it's good, but i'm stuck in chapter 6 page 341 let $$ dX_t=a(X_t)dt+b(X_t)\,dW_t $$ they said that $$ \int_{t}^{t+\Delta t}a(X_{u}) \, ...
3
votes
4answers
188 views

Using $(1+x)^k \approx 1+kx$ to approximate?

Use the approximation $(1+x)^k \approx 1+kx$ to estimate $(1.0003)^{26}$ and $\sqrt[4]{1.006}$. I know how to solve this step-by-step, but I don't understand what I'm doing exactly: why does ...
0
votes
1answer
48 views

Order of magnitude of a variable.

What will be the order of magnitude of a variable whose value varies between 0 and 1? And why?
2
votes
3answers
53 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
22 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
151 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
2k 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
661 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
81 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
201 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 $e$ ...
3
votes
1answer
805 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 ...