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Questions tagged [computational-mathematics]

This tag concerns computational problems central to mathematical and scientific computing. The scope includes algorithms, numerical analysis, optimization, and linear algebra, computational topology, computational geometry, symbolic methods, and inverse problems.

Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. Subtopics include numerical linear algebra, numerical optimization, computational geometry, numerical PDEs and inverse problems.

Consider also posting your question at Computational Science Stack Exchange.

1729 questions
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What algorithm is used by computers to calculate logarithms?

I would like to know how logarithms are calculated by computers. The GNU C library, for example, uses a call to the fyl2x() assembler instruction, which means that logarithms are calculated directly from the hardware. So the question is: what…
zar
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73
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8 answers

incremental computation of standard deviation

How can I compute the standard deviation in an incremental way (using the new value and the last computed mean and/or std deviation) ? for the non incremental way, I just do something…
shn
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61
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18 answers

Unsolved Problems due to Lack of Computational Power

I was recently reading up about computational power and its uses in maths particularly to find counterexamples to conjectures. I was wondering are there any current mathematical problems which we are unable to solve due to our lack of computational…
user671231
61
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3 answers

Is "A New Kind of Science" a new kind of science?

A couple of years ago I was reading "New Kind of Science" (NKS) by S. Wolfram, and it presented lot of interesting ideas for a young Physics undergraduate. Now that I am studying Mathematics however, I realise that many ideas of NKS seem to be not…
Andrea
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57
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3 answers

What is the formula for pi used in the Python decimal library?

(Don't be alarmed by the title; this is a question about mathematics, not programming.) In the documentation for the decimal module in the Python Standard Library, an example is given for computing the digits of $\pi$ to a given precision: def…
ShreevatsaR
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35
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Rapid approximation of $\tanh(x)$

This is kind of a signal processing/programming/mathematics crossover question. At the moment it seems more math-related to me, but if the moderators feel it belongs elsewhere please feel free to migrate it. I'm working on a project where I have…
Bitrex
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25
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5 answers

How could I improve this approximation?

In a computer application, I need to solve trillions of times an equation which can be reduced to $$f(x)=\sin(x)-a x=0$$ Newton methods (quadratic and higher orders) are used for the solution. Parameter $a$ is random and the solution $x$ looked for…
Claude Leibovici
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25
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8 answers

Fastest Square Root Algorithm

(edit, 9 years later... hello smart contract developers, I know that's why you're here lol) What is the fastest algorithm for finding the square root of a number? I created one that can find the square root of "$987654321$" to $16$ decimal places in…
Albert Renshaw
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22
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1 answer

Computing (on a computer) the first few (non-trivial) zeros of the zeta function of a number field

If $K$ is a number field, whose Galois closure over the rationals has degree 24 or so, and whose discriminant is around $163^4$, then what is a numerically efficient way of computing the first few zeros of its zeta function on the critical line? I…
Kevin Buzzard
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Efficient computation of $\sum_{k=1}^n \left\lfloor \frac{n}{k}\right\rfloor$

I realize that there is probably not a closed form, but is there an efficient way to calculate the following expression? $$\sum_{k=1}^n \left\lfloor \frac{n}{k}\right\rfloor$$ I've noticed $$\sum_{k=1}^n \left\lfloor \frac{n}{k}\right\rfloor =…
Thomas Ahle
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21
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2 answers

Gauss-divergence theorem for volume integral of a gradient field

I need to make sure that the derivation in the book I am using is mathematically correct. The problem is about finding the volume integral of the gradient field. The author directly uses the Gauss-divergence theorem to relate the volume integral of…
Mohamed Ouda
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21
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1 answer

Product of primes mod n

Let $n$ be an odd composite number. I'm trying to compute $$ f(n)=\prod_{n/2
Charles
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20
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Quadratic sieve algorithm

I am stuck with the sieving stage of Quadratic Sieve algorithm. I've read lots of papers to this point but I can't find any guidlines how to choose sieving interval or how sieving is actually done because what I've seen so far is 'we pick a sieving…
Sergei G
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Calculating logs and fractional exponents by hand

In view of what we can compute by hand, on a piece of paper, without having to use a computer or a calculator, how far can we go with the evaluation of $\log$-functions and fractional powers? More concretely, are there practical methods, that work…
user929304
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19
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5 answers

What interesting open mathematical problems could be solved if we could perform a "supertask" and what couldn't?

If we had a computer that could perform a countably infinite number of steps of a Turing machine, what currently open problems could we solve? I guess a lot of number theory problems could be solved just by verifying it for each $n$. But presumably…
Seamus
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