# Tagged Questions

**7**

votes

**1**answer

221 views

### Compute an arbitrary decimal place of $\pi$

Is there a method to find the value of the $n$-th decimal place of $\pi$ which is more efficient than having to compute all decimal places before as well?

**8**

votes

**1**answer

290 views

### Fast checking that overdetermined polynomial system does not have a solution

As a result of some inductive procedure for each $n$ I have a system of about $n^2$ polynomial equations with $n$ variables with integer coefficients, which can be precisely computed. As the system is ...

**6**

votes

**2**answers

266 views

### Rigorous numerics for maxima and minima (one variable)

Let $f:\mathbb{R}_0^+\to \mathbb{R}$ be defined by some combination of the four basic operations and square roots. (The argument of square-roots is assumed is to be non-negative, and the value of ...

**2**

votes

**1**answer

166 views

### Reducing the error of Algorithms by assigning variables formulas instead of values

Let me first give the intuition for my question: Suppose that you want to use a ruler to mark $n$ points in a line on a page, with 1 cm distance between neighbor points. There are two ways:
1- Mark ...

**2**

votes

**1**answer

312 views

### Complexity of computing derivatives

Sorry if this is too simple. This is my first question here.
Suppose $f : R^n \to R$ is a differentiable function. Say that we can compute in $T$ arithmetic operations the value $f(x)$ at any point ...

**3**

votes

**1**answer

234 views

### Numerical Beta Function

Anyone know a fast and concise way of calculating the Beta $B(a,b)$ function for smallish (<10) real $a$ and $b$.
For integer $a$ and $b$ I have:
$B(a,b) = \prod\limits_{j=1}^b \frac{j}{a+j}$
...

**5**

votes

**6**answers

3k views

### Fast evaluation of polynomials

Hello everybody !
I was reading a book on geometry which taught me that one could compute the volume of a simplex through the determinant of a matrix, and I thought (I'm becoming a worse computer ...

**5**

votes

**3**answers

522 views

### Appropiate models of numerical computation

Hello,
in contrast to the more discrete part of computational mathematics (cryptography, combinatorial computation), numerical mathematics seems to ignore typical questions of theoretical computer ...

**1**

vote

**2**answers

723 views

### Verifying a sequence that converges to pi [closed]

A computer program ouputs the digits of $\pi$ by evaluating the recurrence relation
$a_{n+1} = a_n + sin \ a_n$
with $a_0 = \frac{6}{5}$
Does the sequence actually converge or is this just ...

**5**

votes

**1**answer

3k views

### Meaning of \Subset notation

The symbol $\Subset$ (occurring in places where $\subseteq$ could occur syntactically) comes up frequently in a paper I'm reading. The paper lives at the intersection of a few areas of math, and I ...

**1**

vote

**2**answers

756 views

### What is the right citation for the power iteration method to find eigenvalues?

What is the right citation for the power iteration method to find eigenvalues, if I want to cite the method in a paper? I've seen some Google PageRank references in this context. But Brin and Page ...

**30**

votes

**7**answers

2k views

### What is the time complexity of computing sin(x) to t bits of precision?

Short version of the question: Presumably, it's poly$(t)$. But what polynomial, and could you provide a reference?
Long version of the question:
I'm sort of surprised to be asking this, because ...

**-2**

votes

**4**answers

10k views

### How to write IF…ELSE as mathematic equation? [closed]

I'm writing a computer program and I need to fit some IF..ELSE condition into mathematic model, so I can't use regular programming constructs. For example, how would I turn this into mathematic ...