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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.

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1945 questions
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Sound attenuation formula

I have some problem with the formula used for sounds spatialization in a framework I use (SFML). For displaying a sound in 2D, I'm drawing a circle (its radius is the distance where the sound's volume is 100%), and I'm trying to draw a border to…
Bloo2
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How many possibilities for a numerical PIN with no more than 9 digits?

I understand that there would be 1,000,000,000 possibilities for a PIN of exactly nine digits (10^9, ten being the vocabulary (0-9) and the power of nine being the length of the PIN), but what about for a pin of 9 or less digits? I am a computer…
user6336941
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Find all vectors with magnitude between $n-\delta$ and $n+\delta$

I am working on an program to compute the structure factor of a given configuration of 3D points, and I need an efficient algorithm to generate all the possible 3D vectors with integer coordinates and magnitude between $n-\delta$ and $n+\delta$,…
valerio
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function computed by programs

I have two questions: Which is the function computed by the program $o^1_1(Succ, Succ)$? Which is the function computed by the program $\mu^1(\pi^2_1)$? where $o^n_m$ for the composition rule $Succ$ for the successor rule $\mu^n$ for…
Kasia
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How to solve the hypotenuse of a Right Triangle when the adjacent is unknown and the other leg is given?

I already know how to solve a hypotenuse when both leg and adjacent are given. But my instructor gave as an assignment which is to find the hypotenuse. The problem is this: One leg of a right triangle is 24 inches ($a$) long and the hypotenuse is…
iAthena
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Calculate height for rows of rectangles within a given width

I have an array of rectangles, all of the same height, but with different widths. Imagine they are on a single line with a uniform gap between them as shown below... |XXX| |X| |XXXXX| |XXX| |XXXXX| |XXXX| |XX| Lets say the rectangles are…
Michael
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Golden Section Search termination condition

From textbooks I found that the tolerance for Golden Section Search method should be set to $\sqrt{\epsilon}$, where $\epsilon$ - is the machine epsilon. This can be derived from Taylor series. So, in other words, setting tolerance less then…
atah1991
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Simple way to find square root of perfect squares

Let me first explain my problem: I am trying to write a program that can generate operations that compare a set of data rather than pulling from a list of possible relations. I have it to the point where it can generate exponentiation but I think…
0ctoDragon
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How can I solve for r?

How can this be solved: Using the Geometric Series Sum formula: $S_n = \frac{a (r^n-1)}{r-1}$ It is impossible to get $r$ with normal algebra. But with other methods it is possible. for example to find $a$ it would look like this with normal…
Hanno kruger
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Rounding of an integer multiplied by a decimal

Had a question regarding numerical rounding that I hope can be answered. Is there anyway to prove the following: For any non-zero constant a, prove that x - round(round(x * a) * (1/a)) == 0 I have been playing with the case in python with: for x…
ssnake
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Design Turing machine for 2^n

Design a Turing machine to compute the function p(n)=2^n I know how to write a code for the function 2n, but I am stuck with writing n copies of 2. Can anyone help me out? Thank you very much.
Deepsea234
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What is the largest real number that can be made from using 7 characters?

All operations (multiplication, exponentiation, factorials, etc...) can be used including such functions as the busy beaver.
pokerlegend23
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Negation of this mathematical expression: $x + y > z$

What is the negation of this mathematic expression: $(x + y) > z$. I want to apply negation to the whole statement i.e. $\neg \big((x + y) > z \big)$ What will be the answer?
Namra Saheba
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