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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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Simple Error Question

I have a question which asks to find the absolute error and then asks if the actual error agrees with the theoretical error bound. Am I missing something or are absolute and actual error the same thing?
user140152
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How would I convert from frequency back to percent?

I'm working on a web application that uses an oscillator. It has a parameter that goes from 0 to 100 percent. I translate that percent into hertz using this equation: $$ \text{frequency} = 2^{(\lfloor 128*\text{percent} \rfloor - 69)/12}*440 $$ I…
Awk34
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Navier Stokes FDM: Iterative Solvers (Component Form vs Matrix Form)

I hope you are all enjoying a pleasant holiday season, if you happen to be celebrating. Currently, I am engrossed in a university assignment that involves conducting a benchmark with various solvers such as Jacobi, Gauss-Seidel, and the Conjugate…
natsukashi_heiwa
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How to solve the follwing inequality? some conditions of parameters.

Assume that the following inequation exist. How can I get the condition of parameters? $$(b_1-\frac{1}{2}u_1)u_1\geq (u_1+u_2)(t-t_0)+x_0$$ $$u_1\in[0,b_1]$$ $$u_2\in [0,b_2]$$ $$x_0\geq0$$ and $b_1,b_2$ is a constant Numerical solution, $$b_1=400,…
Yang
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Performing ϵ-closure on NFA

Say you have an NFA where the only transitions from the start state are $\epsilon$, when performing an $\epsilon$-closure then you have a state that is completely isolated and I'm not sure if my understanding is correct, because the result doesn't…
user1164719
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A matrix iterative inequality problem

We want to solve the linear system $Ax=b$, where $A$ is a SPD and approximate the solution $x_*$ by the following iteration. $$\begin{cases}x_{k+1}&=\arg\underset{x\in x_k+span\{e_{i_k}\}}{\min}||x-x_*||_A\\ i_k&=\arg\underset{1\le i\le…
James Chiu
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How to determine parameters that satisfy a given equation (using python)

I am working for a mathematical model in which I intend to fit the model itself to statistical data to determine the values that my parameters must have. I am dealing with equations of the sort: $$0.001=\frac{e^be^{-c}}{1-\int_0^9{e^{at}}dt}$$ and I…
Nick Heumann
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How to add N steps between 2 ranges of learning rates

I want to have a list of 5 learning rates. My min LR is 1e-6 and my max LR is 1e-4. I want to have 3 LRs in between so that they are evenly distributed. LRs = [1e-6, ..., ..., ..., 1e-4] Sorry if this is a very elementary question but what could be…
Levent Ozbek
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How do I calculate the exponent of a certain number without multiplying it by itself over and over again?

I have a number 'x' raised to 'n', and I want to calculate the x^n without x.x.x.x....(n times). How do I do that? Is it possible to do it without the tedious self-multiplication? (I mean to do it without computers) I've been suggested using…
DARK Energy
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Find all points where the gradient of a high-dimensional function are equal to zero in some domain, numerically

I was wondering if anybody was aware of a numerical method to find all points where the gradient of a high-dimensional function are equal to zero in some domain. Thanks
Maksim
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Time filter for leapfrog method with a highly nonlinear coupled system of PDEs

Does anyone know how to use time filter with a system of equations like $i\dot{\phi} = \chi$ $i \dot{\chi} = - f(\phi)?$ I looked up higher order Robert Asselin filter but the only example I found was a single linear equation however in the…
Sachin Vaidya
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Prime Numbers...

Are there any functions whose output is a prime number? For eg. The function $x^2$ spits out squares of $x$; is there a similar function for Prime Numbers as well(which gives output as Prime Numbers)?
Some 1
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modulo with very large numbers and non-integer components

I'm trying to find the modulo of a very large number using Fortran. The number is larger than the precision available. Example: [ 1e40 x log(2) ] modulo pi I hoped there would be some clever theorem out there for a problem like this.
Ashley Brereton
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Finding Tax amount after fixed amount discount off

I'm trying write a function that calculates cart totals. I'm crosschecking above calculation which is correct. I have a cart total which is 115.32 dollar. I apply 20 dollar fixed discount off. The sale tax is 9%. What I'm trying to find is to find…
Caner
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How many games required to achieve a specific number of points (win = 1 point , loss = -1 point)

I'm not a mathematician, so hoping to get some help, I wouldn't be surprised if you all found this very trivial! I'm playing a game that awards 1 point for a win, but subtracts a point for a loss. I'd like to know how many games I'd have to play to…
Ross
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