# Tagged Questions

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### Numerical evaluation of Hurwitz zeta function

Is there a way to evaluate numerically the Hurwitz zeta function $$\zeta(s,a) = \sum_{n=0}^\infty \frac{1}{(n+a)^{s}}$$ that is more efficient (i.e., quick and precise) than simply explicitly adding ...
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### How to generate a point cloud with known symmetry?

So I would like to know if there are any published algorithms to generate point clouds with known symmetry groups, such as $D_{3h}$ or $O_h$ and stuff like that. I know lots and lots of point clouds ...
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### Algorithm for retrieving all the permutations (randomized) for a vector sequence 1…N with only unique values

Here is the problem: I have a vector of $N$ elements long (containing only unique values from $1...N$). I am searching for an algorithm to obtain all the (randomized) combinations possible, where ...
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### Fastest Algorithms for Determining the Nullity of a Matrix

How exactly does one go about determining the Nullity of a Matrix quicker than simply running Gaussian Elimination on the matrix itself? To be perfectly honest I can't think of a method that doesn't ...
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### Global optimization

Assume that I want to find the global minimum of a non-linear, non-convex, multidimensional function subject to several restrictions. Could you recommend me any deterministic strategy which can ...
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### Parity of number of factors up to a bound?

Consider $b,n\in\mathbb{N}$ where $b\leq n$. We want to find the parity (ie. odd or even) of the number of divisors of $n$ that are $\leq b$. The question is to find a fast algorithm to find that ...
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### What's a method of finding when a repititious multi-dimensional function repeats when clamped?

Here's some code. Don't try to understand it, but refer to it: ...
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### Solve non-linear equations of 3 variables using Newton-Raphson Method iterms of c,s and q.

The three non-linear equations are given by $$c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0$$ s[2.001 *c + 835(1-q)]-2.001*c =0 ...
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### Fast algorithm for approximating Eigenvalue distribution of large sparse matrix

I am interested in the eigenvalue distribution of a huge $2^{16}$x$2^{16}$ Hermitian sparse matrix with spectrum contained in $[-1,1]$. That is I don't need to know all eigenvalues exactly, but rather ...
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### What initial guess is used for finding n-th root using Newton-Raphson method?

I would like to know what is an optimal initial guess for use with Newton-Raphson method when finding n-th root. I develop some program which uses GMP C++ library. GMP manual says: The initial ...
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### Laguerre's method and zero division

I'm trying to understand Laguerre's method for root finding and I have hit one road block. Suppose I have a polynomial $p(x) = x^4 + 1$ and an initial guess $x_0 = 0$. This results in division by ...
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### How to choose the starting point in Newton's method?

How to choose the starting point in Newton's method ? If $p(x)=x^3-11x^2+32x-22$ We only learnt that the algorithm $x_{n+1}:=x_n-\frac{f(x_n)}{f'(x_n)}$ converges only in some ...
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### Checking convergence of an iteration

How to check if an algorithm converges in an interval, for example $x_{k+1}:=\frac{1}{11}(1-\cos(x_k))$ does it converge for any startpoint $x_0\in (-\pi/2,\pi/2)\setminus\{0\}$ ? (as hint: ...
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### Newton's method for polynomial interpolation

I've seen that in Newton's method for interpolating polynomials, the coefficients can be found algorithmically using (in Python-ish): ...
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### Algorithm for finding power

I has been searching for a high precision library in PHP to do calculations like $$232323232323^{121212.2232323232}$$ etc (ie, with very large numbers, including decimals), but failed to get any. ...
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### Need Help! Recognizing types of errors: Truncation and Roundoff

I am a little unclear on the difference between the two. What exactly are they? As simplified as possible :) How can i recognize them and identify parts of formulas or algorithms that would give ...
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