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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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Integration of the $\int_{0}^{1}e^{\frac{\kappa}{\alpha} y^{\alpha}}y^{\beta}(1-y^2)^{\frac{d-3}{2}}\text{d}y$

Does one calculate the following integral: $$B_{d}(\kappa, \alpha, \beta) :=\int_{0}^{1}e^{\frac{\kappa}{\alpha} y^{\alpha}}y^{\beta}(1-y^2)^{\frac{d-3}{2}}\text{d}y$$ where $d,\kappa, \beta >0$ and $\alpha \in (0,2]$ Thanks in advance:
M.cadirci
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Romberg Method making my approximation worse

I have the following function: $$\frac{1024\,x^4}{e^{(4x)^{4}}}$$ And I applied the composed Simpson rule to obtain the value of the integral of that function from $0$ to $0,62715.$ Then, I applied the Romberg Method to obtain a better…
Ru44Be4N7
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Rewrite $\ln x - 1$ and $\log x - \log(1/x)$ to Avoid Lost of Significance

As question in the title, how should I rewrite $\ln x-1$ and $\log x - \log (1/x)$ in a way that can avoid the loss of significance? I have tried to use the taylor series expand the lnx - 1 and my answer is $$\dfrac{6(x-2)- 3(x-1)^2+ 2(x-1)^3}{6}$$…
Hanyi Koh
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Negative power of inequality

We know the following inequality, \begin{equation*} (a+b)^{\alpha}\leq a^{\alpha} + b^{\alpha},\quad a,b \geq 0, \quad \alpha \in [0,1]. \end{equation*} Is it possible to write the following elementary inequality. If so, how we…
M.cadirci
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Speed and Time - finding average speed

A person wanted to travel from charbag to aalambag with an average speed of $60$km/h by car. The distance between the two cities is $2$ km. Due to traffic he could travel at $30$ km/h for the first km. What should his speed be for the remaining…
Pawan Bhatt
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-a^b and pedmas/bodmas order of operation?

Really silly question but didnt know where else to ask. I am looking back at some basic definite integration stuff and have stumped myself at the most basic of things (I have a knack for doing this kind of thing to myself). Lets say I am met with…
Jam
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Different database queries

We have the table person (pid,pname) We want to find the names of the persons. What is difference between a and d? I know that d is the correct answer but I don't understand why. $$a)\, \{\langle X\rangle \mid \forall Y\,…
Krister
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If $f = ax - by + 0c$, with non-negative $x$, $y$, $c$, and $x+y+c=n$, all integers, then how many distinct values does $f$ take?

Given a function $f = ax - by + 0c$, with constraints $y\geq 0$, $x\geq 0$, $c\geq 0$, and $x+y+c=n$, where all are integers. I am interested to find the count of all unique values of $f$. I know that total number of different arrangements of $a$,…
Resorcinol
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Formula for this point distrubution on a sphere?

A series of points are plotted on a unit radius sphere, see image above. Each point represents a vector coming from the origin. First, points on XY and XZ planes are created using a certain equal angle increment for fi and theta respectively. Then…
alikim
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How to find top 3

If i have 25 horses in one race you can tack 5 horse only, if you want find top 3 horse from this 25 horses than how many race you need for find top 3 horse from it?
user513264
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If I have a function that recurses on fibonacci numbers, can I determine how many times it recurses?

Lets say I have the following function: function fib(n) { if (n <= 1) return n; return fib(n - 1) + fib(n - 2); } For $n = 5$, it calls itself $14$ times. For $n = 4$, it calls itself $8$ times. Is there a formula to figure out how many…
Human Cyborg Relations
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Show that for any constants $k$ and $j$, where $j > 0$, $(n+k)^j = \Theta(n^j)$

Does this solve the question: There exist $c, n_0$, such that $(n+k)^j = n^j$ for all $n>=n_0$ I tired the above but couldn't find an answer..
user483926
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Computational Methods: Explain how to evaluate the following functions accurately for small |x|

Please help me solve this problem. I have a difficult time understanding my professor and need assistance on my homework assignment so I can be prepared when the exam comes. The question is as follows- Explain how to evaluate the following functions…
BCarey
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How to find three natural numbers $n_1, n_2, n_3$ with $n_1 < n_2 < n_3$ such that $n_1 + n_2 + n_3 = 784$ and $n_1^2 + n_2^2 = n_3^2$

How to calculate the multiplying of the three numbers $(n_1, n_2, n_3)$ where the summation of them equals 784 if you know the followings: $n_1, n_2, n_3$ are natural numbers $n_1 < n_2 < n_3$, $n_1^2 + n_2^2 = n_3^2$
omar.sayed
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Need to solve for $x$ in equation with XOR and Bit Rotation (Circular Shift)

I'm not the best with math and I've been needing to solve this equation which includes the XOR operator for 32 bit integers and some bit rotation (circular shifting). $y$ = ($x$ ⊕ 32757935 * $i$ ⊕ ROR($x$, 3) ⊕ ROL($x$, 7)) Where ⊕ is the XOR…
Slappy826
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