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

learn more… | top users | synonyms

0
votes
0answers
19 views

I need help with the Von Neumann Stability Analysis for this specific PDE

I've been working on this question $\frac{\delta u}{\delta t} = \frac{\delta^{2} u}{\delta^{2} x}-\lambda \frac{\delta u}{\delta x}$ where $\lambda = 3 $ After discretising the PDE I have $\...
0
votes
0answers
19 views

How to mathematically model a realistic aperture illumination?

I want to know a mathematical expression that i can use to model a realistic aperture illumination to produce the primary beam of an antenna so that the radial distribution of this aperture ...
2
votes
1answer
30 views

mathematical patterns and their connection to grouping “things”. [closed]

The heading of this is probably misleading as I know group has a well defined mathematical definition, yet I know not what it is. My question is very open ended, I hope you all don't mind. If we ...
2
votes
0answers
54 views

Summation of n terms of a series$ 1+2+8+64+…$

In one of my problem , I got a series as $1$,$2$,$8$,$64$,$1024$...and so on. can we really get a sum expression for that series$???$ If yes, then what is the expression $f$ $?$ or the sum of $n$ ...
0
votes
0answers
24 views

What do we call the harmonics in a discrete Fourier series representation?

In harmonic analysis using discrete Fourier series, if I'm using the 0f, 1f, 2f, 3f and 4f for representation where f = frequency, what is the correct way to say how many harmonics I'm using for ...
5
votes
4answers
723 views

Write number as a power of 10

Just to clarify, I'm not interested in Standard Form/Scientific notation. Is it possible to write a number as a power of ten, so that for example it would look like this? ...
3
votes
1answer
177 views

Given 3 random points, what is the probability of these two situations involving a perpendicular bisector and distances?

Suppose we're given 3 random points $p_0=(x_0,y_0),p_1=(x_1,y_1),p_2=(x_2,y_2)$ from a two-dimensional continuous uniform distribution $\{U(a,b)\}^2$, for some $(a\in\mathbb{R})\lt (b\in\mathbb{R})$, ...
0
votes
0answers
18 views

how to find the total amount depends specific percentage

I have to find an easier way to find the net amount that makes the base amount after calculating the percentage. For example I have an amount of $70000$ and I want to know the actual amount that add $...
1
vote
2answers
38 views

How do I go about computing the distance between a point and a line in 4-D?

The point p = (1,1,1,1) ∈ R^4 (real numbers) to the line L(a) with a = (1,2,3,4) in particular. I tried it as follows: The distance d(p,L(a)) is the orthogonal projection of p onto L(a). So the dot ...
0
votes
2answers
48 views

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 ...
12
votes
1answer
205 views

On the prime-generating polynomial $m^2+m+234505015943235329417$

In 2009, J. Waldvogel and Peter Leikauf found the remarkable Euler-like polynomial, $$F(m)=m^2+m+234505015943235329417$$ which is prime for $m=0\to20$, but composite for $m=21$. Define, $$F(m)=m^2+...
0
votes
0answers
32 views

data for zeros of the derivative of the Riemann zeta function

People have computed a large number of zeros of the Riemann zeta function. Do we have data for zeros of the first derivative of the Riemann zeta function?
0
votes
1answer
20 views

Fast Fourier transform with a different product function

Problem Given 2 N degree polynomials as $$a_0 + a_1x+a_2x^2+...+a_Nx^N $$ and $$b_0 + b_1x+a_2x^2+...+b_Nx^N $$ Assume no 2 coefficient are same in the 2 polynomials. Find the product of the ...
3
votes
0answers
118 views

Computing the density of a set of multiples

I have a finite* set $A=a_1<\cdots<a_r$ of positive integers. Define $B$ as the set of positive integer multiples of $A$ and $$ A_1=\frac{1}{a_1} $$ $$ A_k=\frac{1}{a_k}-\sum_{i<j<k}\frac{...
2
votes
3answers
70 views

Computing the tail of the zeta function $\sum_{n>x}n^{-s}$

I want to compute $$ f_s(x)=\sum_{n>x}n^{-s} $$ for some $s>1$ (in my case, $s=3$). Of course $$ f_s(x)=\zeta(s)-\sum_{n\le x}n^{-s} $$ but for $x$ large this is hard to compute. Are there good ...
0
votes
1answer
261 views

Rotations of a cube

I am trying to create a program using Python 3 which must simulate the rotations of a cube. However, I am struggling to figure out how to rotate that cube. I have the following formulas: ...
0
votes
0answers
54 views

What is the physical significance of arithmetic operations?

Here is an example of what I mean by physical significance: When we use some geometric or trigonometric identity, let us say Pythagoras' theorem to calculate the length of the diagonal of a field, ...
0
votes
0answers
160 views

Pseudo-arclength continuation scheme

I have implemented a simple parameter continuation scheme to find the stationary solutions of a nonlinear problem at different parameter values. However, my scheme cannot handle bifurcations - it ...
-2
votes
2answers
70 views

What are good techniques for creating a DFA state diagram given a set of accepted/rejected strings?

I am in a Discrete Structures class and my teacher is pretty big on proving his intellect to the class and getting an average of about 60% for his test questions. Right now we are working with ...
4
votes
1answer
70 views

What mathematics topics pertain more towards applied mathematics?

I'm entering my second year of undergrad (majoring in mathematics), and I've found that I am really bad at Linear Algebra, but very good at Calculus and Differential Equations. I'm hoping to venture ...
1
vote
2answers
93 views

How can you expand the adjoint of a matrix into a polynomial with matrix coefficients?

This book contains an algorithm which claims that a matrix $sI - A$, where $A$ is some $n \times n $ square matrix and $s$ a variable can be expanded into $$adj(sI - A) = K_0 s^{n-1} + K_1 s^{n-2} +.....
0
votes
0answers
35 views

Quantify difference between regularity and irregularity

I am solving an equation numerically on a 1D-domain using the finite-element method. I am solving it using two different domains, one regular and one irregular. Naturally, the solution varies slightly ...
0
votes
1answer
33 views

Stability of (floating point) computed variance

Homework Question from Accuracy and Stability of Numerical Algorithms, 2nd Edition, by Nicholas J. Higham, page 33: So every time we store an number and do a operation, we introduce an error bounded ...
0
votes
0answers
33 views

How can I modify this simple code to include the pressure term? (1-D Navier Stokes)

I have a mathematical model that involves a cylindrical container that is being modeled with a one dimensional simplification as the system is isotropic with respect to the z-axis. As part of the ...
2
votes
0answers
75 views

I have a finite permutation group and access to a computer algebra system, how can I recognize the structure of the group?

I have a fixed permutation group $G$, and cannot tell which finite group it really is in a "human readable" way. I also have GAP. Is there a step by step computation to give me the structure of this ...
3
votes
1answer
64 views

Finite difference method works for $\frac{\partial u}{\partial t} = \frac{du}{dz}$ but not for $\frac{\partial u}{\partial t} = - \frac{du}{dz}$?

I am using the method of lines with forward differences to solve the transport equation $$\frac{\partial u}{\partial t} = \frac{du}{dz}$$ with initial condition $u(z, 0) = z$ and boundary condition $...
2
votes
0answers
21 views

How to compute Generalized Group Inverse?

Given a transition matrix $P \in \mathbb{R}^{n \times n}$, i.e. $\sum_j P_{ij} = 1$ and $P_{ij} \geq 0$ for all $i,j$. One can show that there exists a unique group inverse $B$ of $A:= I - P$ which ...
1
vote
0answers
21 views

Minimum vertex cover of vertex disjoint odd holes and antiholes

I am interested in knowing whether the minimum vertex cover of a graph that can be written as the union of vertex-disjoint odd holes and odd antiholes can be found exactly, in polynomial time. I could ...
0
votes
0answers
46 views

How to use the false-position method

I have two equations; 1) $$ 0 = 7x+13$$ and 2) $$0 = 2x-13$$ Why can I use the false position/secant method in the first equation, but not in the second? Further, how does one go about using this ...
0
votes
0answers
51 views

Multiplications in determinant of an $n \times n$ matrix?

Assuming we use Gaussian Elimination/LU decomp, is there a general formula to describe the number of multiplications involved in finding the determinant of an $N \times N$ matrix? Find the ...
3
votes
2answers
112 views

An efficient way to find anagrams

Consider a set of words where you want to divide the set into subsets of words, where all members of each subset are anagrams (same letters, different arrangement). You can do this computationally in ...
5
votes
1answer
165 views

Integer solutions to the equation $a^3+b^3+c^3=30$

The following problem was posed to me but I could not do much about it: Determine if there are any integer solutions to the equation $a^3+b^3+c^3=30$ I made a computer search that shows that ...
0
votes
2answers
54 views

Clarification about the concept of number

I am reading a book called Numerical Notation: A Comparative History (by Stephen Chrisomalis). The first chapter (Introduction), second and third paragraph go like this: If you look up from this ...
1
vote
0answers
69 views

How can we calculate the tensor product of Lagrange basis polynomials?

Given data points $(x_i,y_i)$, the Lagrange basis polynomials are $$\mathcal l_j(x):=\sum_{i\ne j}\frac{x-x_i}{x_j-x_i}\;.$$ I'm reading a text targeting Smolyak's algorithm. In this text, they use ...
1
vote
2answers
68 views

Maple not able to calculate Bernstein polynomial

Hope you can help me on this one. Please look at this simple Maple code: Obviously $B(1)=g(1)=4 \neq 0$. Why is Maple not able to compute this right? Am I doing something wrong? Kind regards PS: ...
0
votes
1answer
24 views

Finding the bounds for a truncation error

I have two series, $S$ and $T$ which approximate $\pi$ such that $$S_n = 4 \sum_{i=1}^n \cfrac{-1^{i+1}}{2i-1}$$ and $$T_n = \Big(12 \sum_{i=1}^n \cfrac{-1^{1+i}}{k^2} \Big) ^{\frac{1}{2}}$$ It is ...
5
votes
0answers
87 views

On a unique(?) binomial property of $3003$

Given the triangular number, $$T_k = \frac{k(k+1)}{2}$$ and remembering that, $$\binom{n}{m}=\binom{n}{n-m}$$ Excluding $a_0=1$, we then have the six-fold (at least) equalities, $$\begin{aligned} ...
0
votes
0answers
38 views

How to calculate $det(X^T X)$ efficiently, update one column of X each time

$X_{1} = (A, b)$, where $X_{1}$ is a $n\times p$ matrix, $A$ is a $n\times (p-1)$ and $b$ is $n\times1$. First calculate $\det(X_{1}^T X_{1})$, then update $b$ with $c$, st. $X_{2} = (A, c)$ and ...
2
votes
3answers
62 views

What is the value of this function?

Consider the three-variable function defined at the following way for all natural numbers $n,x,y$ : $f(0,x,y) = x+y $ $f(n,x,0) = x$ $f(n,x,y) = f(n-1, $ $ $ $f(n,x,y-1) , $ $ $ $f(n,x,y-1)+y ) $. ...
4
votes
2answers
213 views

(Fast way to) Get a combination given its position in (reverse-)lexicographic order

This question is the inverse of the Fast way to get a position of combination (without repetitions). Given all $\left(\!\!\binom{n}{k}\!\!\right)$ combinations without repetitions (in either ...
0
votes
0answers
66 views

Need to solve for an angle, do I need to use numerical methods??

I need to run a simulation on MATLAB where I need to solve two equations for two unknowns. The equations look something like this, $$x_{comp} = G\cdot \cos^2 b \cdot \cos(a+b).$$ $$z_{comp} = G\...
1
vote
1answer
130 views

Expected Utility Method and a Repeated Game Solution [closed]

I am trying to replicate Bruce B. de Mesquita's (BDM) results on political game theory for prediction. Based on where actors stand on issues, their capabilities, salience, BDM's method attempts to ...
6
votes
3answers
267 views

Fast way to get a position of combination (without repetitions)

This question has an inverse: (Fast way to) Get a combination given its position in (reverse-)lexicographic order What would be the most efficient way to ...
0
votes
1answer
331 views

Constructive Induction to derive and prove the formula for a geometric sequence

$\sum_{i=1}^nr^i = a \cdot (b^n) + c$ Base Case: n=1, this holds Inductive Hypothesis: Assume for $n = k$, $k \ge 1$ that $\sum_{i=1}^k r^i = a * (b^k) + c$. Inductive Step: Prove for $n = k+1$ ...
0
votes
0answers
35 views

In bipartite directed graph, how to efficiently find nontrivial edge values such that for each node, sum of edge values is zero?

Suppose I have a set of sources U and a set of sinks V and a set of directed edges E going from elements of U to elements of V. I want to find a vector z of size |E| (each value of z is assigned to ...
8
votes
1answer
133 views

Are the unit partial quotients of $\pi, \log(2), \zeta(3) $ and other constants $all$ governed by $H=0.415\dots$?

Khinchin showed that given the simple continued fraction of a real number, $$r = a_0+\cfrac{1}{a_1+\cfrac{1}{a_2+\cfrac{1} {\ddots}}}$$ then it is almost always true that the partial quotients $a_i$ ...
0
votes
1answer
56 views

Seeking the Recommendation on Complexity Theory books

S.E advisers, I am a rising college junior in US with a major in mathematics and an aspiring applied mathematician in the fields of theoretical computing. I just recently got a research project on ...
0
votes
0answers
22 views

How can I measure the dispersion of a discrete time system?

I have a discrete time system: x[n+1]=A*x[n]+B[n], with B[n] as an excitation signal. How can I measure the dispersion of this system? I guess this is related to some property of A, which depicts the ...
2
votes
2answers
98 views

Verify input is the sum of other numbers

I have a relationship: 4000k + 2500j + 400g = n, k >= 0, 0 <= j <= k, 0 <= g <= j I have to, given n, verify ...
2
votes
1answer
85 views

How do computers generate primes so quickly?

From what I understand, when a computer encrypts a file using an encryption standard like RSA, one of the steps is to generate two large primes, and multiply them together. I have created RSA keys on ...