All Questions
Tagged with computer-science na.numerical-analysis
21 questions
4
votes
1
answer
341
views
rank of an integer valued matrix
I make some numerical experiments, involving rank of integer valued matrices of the size about $14\times 24$. As the matrix is integer valued, theoretically there should be no room for errors. However ...
- 728
3
votes
1
answer
308
views
Root finding algorithm for an analytic function
Given an analytic function $f(x)$. What is the best algorithm to find roots on the interval $[a,b]$ inside the radius of convergence> What is its complexity with respect to the length of input of ...
- 81
4
votes
0
answers
214
views
Computational complexity of zeros of an analytic function
The work of Friedman and Ko, page 342, Corollary 4.3.1
states that all zeros of analytic polynomial time computable function are polynomial time computable, but for me that is not clear how it could ...
- 81
11
votes
3
answers
726
views
Can computers find zeros of order $2$?
We assume we are given an entire function $f: \mathbb C \to \mathbb C$ with $f(0)=1$ and $f'(0)=0$ and $f$ is real on the real axis.
We assume (as a fact about $f$, that we want to demonstrate ...
- 124
0
votes
0
answers
89
views
3D interpolation function
I've got a 3D figure created using around 30k points and has different regions colored in an specific way according to some unrelated variables that come from a project I'm creating. Taking in ...
2
votes
3
answers
415
views
Efficiency of representations of number
In everyday practice the most common ways to represent integers are the binary and decimal systems. We use floating point or fixed point systems to (approximately) represent the reals. There are some ...
- 3,322
1
vote
1
answer
3k
views
Finding t vlaue in Bezier curve [closed]
According to this question, I'm looking for some method to find the t value in Quadratic bezier curve equation:
$$
B(t)=P_0+t(1-t)P_1+t^2P_2 \space \space where \space 0 ≤ t ≤ 1
$$
In this ...
- 111
1
vote
0
answers
59
views
Open volumetric time series data set
Does anyone know where I can find a good open volumetric time series data set?
I had a look at some of Stanford's open data sets (https://graphics.stanford.edu/data/voldata/ )
But these do not seem ...
- 191
2
votes
1
answer
129
views
cohomology algebra of submanifold in euclidean space
If we write a manifold or CW-complex $X$ as a subset of $\mathbb{R}^n$, in expression of coordinates, for example, \begin{multline}
F(S^2,k+1)=\{(x_1,x_2,x_3,\cdots, x_{3k+1},x_{3k+2},x_{3k+3})\in\...
- 1,990
8
votes
1
answer
330
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?
- 83
10
votes
1
answer
595
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 ...
- 728
7
votes
2
answers
372
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 ...
- 20.2k
2
votes
1
answer
216
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 ...
3
votes
2
answers
2k
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 $...
- 33
3
votes
1
answer
540
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:
$B(a,b) = \prod\limits_{j=1}^b \frac{j}{a+j}$
...
- 144
22
votes
9
answers
17k
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 ...
- 1,654
6
votes
3
answers
632
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 ...
- 5,327
1
vote
2
answers
1k
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 ...
user11822
19
votes
2
answers
11k
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 ...
- 1,601
7
votes
3
answers
2k
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 ...
- 171
46
votes
7
answers
13k
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 ...
- 6,694