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.

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1answer
24 views

Help with Legendre Plot Matlab

I've written a code to change a Chebyshev into a Legendre Polynomial, however it will not plot the graph after and I'm not sure why the graph will not plot? The code i have is: function ...
4
votes
3answers
97 views

How to calculate $10^{0.4}$ without using calculator

How to calculate $10^{0.4}$ without using calculator or if not what is the closest answer you can get just using pen and paper within say $2$ min?
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2answers
32 views

Computing midpoint of an interval overflow

For computing the midpoint m of an interval $[a, b]$, which of the following two formulas is preferable in floating-point arithmetic? Why? When? (Hint: Devise examples for which the "midpoint" given ...
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0answers
13 views

Equivalence and interoperability of computation systems using a calculus

I am trying to prove that two computational systems are interoperable and both can be converted into another parent system . So computational system A,B can be mapped into computational system C. I ...
0
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1answer
35 views

Cannot understand solution (Turing Machine & Reduction)

Photo of my problem that I don't understand About question above in photo, I just can't understand its solution provided. We know the complement of Atm = {...
2
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0answers
17 views

Method to Linearise PDE

I have a Monge-Ampere-type PDE I wish to solve using a finite difference method: $$(1-u_{xx})(1-u_{yy}) -u_{xy}^2 = f(x,y).$$ Is there generally a preferred method for linearising the system after ...
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0answers
21 views

Different methodology for maximizing entropy in continuous random variable case

Suppose we want to maximize the well-known Shannon entropy $S=-∫_{0}^{x_{max}}f(x)lnf(x)dx$ subject to the following constraints $∫_{0}^{x_{max}}f(x)dx=1$, $∫_{0}^{x_{max}}xf(x)dx=x ̅$ and so on ...
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0answers
12 views

Transitivity Proof on graphs: computational or by hand?

I am stuck to transitivity consideration with graphs where $x^a,x^b$ are boolean monomials such as $x_1x_3$ and $x_5$, the cut sets contains $C=\{x^{C_i}=0\mid C_i\in C\}$, ...
2
votes
1answer
67 views

Algorithm for isomorphic groups?

As I understand There can't be a general algorithm to decide if two finite groups are isomorphic, Wikipedia. But are there efficient algorithms for all subgroups of $S_n$ for say $n=10$ or so? ...
0
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0answers
45 views

Problem with 4-body Matlab code

I'm trying to model the 4 body problem to see how Jupiter, Earth and Mercury orbit the Sun. I found a two body script and adapted it as accordingly to modify my problem, but for some reason the ...
4
votes
1answer
40 views

How to simplify this equation regarding pronic numbers for integer solutions

A pronic number is a number that can be expressed as the product of two consecutive positive integers. For instance, $42 = 6 \cdot 7$ is a pronic number. I've become interested in solving for the ...
2
votes
1answer
42 views

Converting Integers from One Base to Another Digit by Digit

So I’ve done some hands-on work with converting integers from one base to another using the well-known method of division and taking the remainder. The most generic algorithm involves dividing the ...
0
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1answer
27 views

Compute Christoffel symbols & Riemann tesors in Maple 17

I invented a metric tensor g and now I'm trying to compute my first Christoffel symbol but an error message is popping up "Error, bad index into matrix" Is there a way for maple to compute ...
0
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1answer
25 views

Method to study obvious properties

Most of the time studying mathematics we come across various properties like associative, commutative,...etc. These properties are obvious and sometimes I feel why at all they are given in the text. ...
2
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0answers
28 views

Algorithm for numerically calculating $\log x$

It was while fiddling yesterday that I came up with this rather pretty approximation: $$\log x = \frac{1}{2\epsilon}(x^{\epsilon}-x^{-\epsilon})+\mathcal{O}(\epsilon^2)$$ To be more precise, ...
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0answers
13 views

Finding All Combinations of a Hierarchical list Where Conditions Are Involved

I want to find all possible combinations of a list that looks like this. a) Option 1 Sub Option 1 b) Option 2 Sub Option 2 c) Option 3 The catch is that there are some simple and some ...
10
votes
2answers
548 views

What does “Mathematics of Computation” mean?

I visited this link: http://www.ams.org/journals/mcom/1950-04-030/S0025-5718-50-99474-9/ And I a bit confused by its title "Mathematics of Computation". I am not a native English speaker. Could ...
1
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3answers
42 views

upper bound of a function $n^{1/\log(n)}$

I have the following expression $n^{1/\log(n)}, \quad where \quad n \in [1, 10,000]$. When I solve this numericall, I get the resultant value 2.718282 for all $n \in [2, 10,000]$. On this basis, I can ...
1
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0answers
26 views

proving euclid's algorithm stops after 2k iterations [duplicate]

Apparently, when initialized on $k$-bit integers $A$, $B$, Euclid's algorithm terminates after at most $2k$ iterations. This result is not immediately intuitive to me. I would appreciate help in ...
2
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0answers
38 views

How to find values of x where $a_i x$ are nearly integers? $a_i \in \Bbb R$

I have a set $\{a_i \in \Bbb R | \ i <=7 \}$, and I'm looking for a way to find values of $x$ where given $\epsilon > 0$, $$\forall i \ \exists n_i \in \Bbb{Z} \ \ |a_i x - n_i| < \epsilon$$ ...
0
votes
0answers
33 views

Find values of x where error term small between rounded and not calculation in non-linear functions f_{i}(x)

Here's my situation. I have a set theory background so I'm out of my league in applied, computational methods so I'd appreciate a hand-up. I have a set of five functions, $f_{i}(x) \ $ where $\ 0 ...
1
vote
3answers
63 views

n(n+1)/2 combinatorial proof (details in description)

Find the number of $2$-lists $(𝑎, 𝑏)$ we can form using the numbers $0,1,2,...,𝑛$ with $𝑎 < 𝑏$. a. Show that the number is $𝑛(𝑛 + 1)/2$ by considering the number of $2$-lists $(𝑎, 𝑏)$ in ...
0
votes
1answer
64 views

About Gröbner Bases

Recently I have come across a book of Gröbner Bases written by Adams & Loustaunau. The book is excellent and I have become interested in Gröbner bases after reading the book. I want to read more ...
0
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2answers
42 views

How to define numbers in a way that a number 'n' is equivalent to the function plus 'n'?

In lambda calculus, is it possible to define (or disprove the existence of) a number system alternative to church numerals such that each number is a function which on application, adds itself to it's ...
1
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2answers
41 views

Linear Algebra matrices question.

Let $A,B$ be 2 square matrices of the same size. And the following holds true $AB=A+B$ How do I prove that $(I-B)$ and $(I-A)$ are invertible
1
vote
1answer
34 views

Explicit piecewise linear approximation of a function of 4 variables

I have a table of numbers for fixed values of 4 parameters $x, y, z, t$, at this $x$ belongs to finite set of natural numbers, $y\in\{1;2\}$, $z\in\{5;10;15;20;25\}$ and $t\in\{1,2,3\}$. Is there a ...
1
vote
2answers
49 views

Big O notation: ratio of two $O(\cdot)$'s is $O(\cdot)$ of the ratio?

Is it true that if $f_1=O(g_1)$ and $f_2=O(g_2)$ then $$\frac{f_1}{f_2}=\frac{O(g_{1})}{O(g_{2})}=O\!\left(\frac{g_1}{g_2}\right)$$ ?
0
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0answers
26 views

Distance Geometry Problem (DGP) Programming Language Recommendation

We have been studying DGPs in clinic recently and I was hoping I might be able to get recommendations for computing languages in the processing of large network solutions. Specific computations ...
1
vote
1answer
38 views

How to write new algorithm of root finding by combining 2 or 3 standard algorithms(bisection, fixed, etc)

I just learned about Bisection Method, Fixed-Point Iteration Method, Newton- Raphson Method, and Secant Method. My prof wants us to be able to write new Algorithm of root finding by coming 2 or 3 ...
0
votes
1answer
36 views

Constructing a specific Rank-One Matrix

Given u $\in \mathbb{R}^{n}$ and v $\in \mathbb{R}^{m}$ with unit $L^{2}$ norm, i.e. $\|u\|_{2}$ = $\|v\|_{2}$ = 1. Construct a rank-one matrix B $\in \mathbb{R}^{mxn}$ such that $Bu = v$ and ...
1
vote
2answers
90 views

Use $\log(x)$ to calculate $\log(x+1)$

Given that I know the value of $\log(x)$, I would like to calculate the value of $\log(x+1)$ on a computer. I know that I could use the Taylor expansion of $\log(1+x)$, but that uses $x$ rather than ...
0
votes
1answer
52 views

One wants to determine $1/(2+\sqrt 3)^4$ having access to an approximate value of $\sqrt 3$.

Can someone help me with this question please: One wants to determine $1/(2+\sqrt 3)^4$ having access to an approximate value of $\sqrt 3$. Compare the relative errors on direct computation and on ...
0
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0answers
35 views

A computation from an article in computational neurosciences (from physical review) which doesn't fit

I am reading this article (with this erratum) in computational neuroscience, and there is a computation there that simply doesn't fit.. Maybe one of you can see something that I am missing? For the ...
0
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0answers
30 views

Hilbert Matrix, Gaussian Elimination with varying pivot strategies, and computation error.

I'm doing a project for my Numerical Analysis class about computational error related to Gaussian elimination, gaussian elimination with partial pivoting, and gaussian elimination with scaled partial ...
0
votes
2answers
20 views

Error analysis on numerical solutiol of an equation

Say I am solving an equation numerically -- the derivatives in the equation I find by a finite difference scheme with an accuracy of the grid spacing $h$. Does this imply that the final solution I ...
2
votes
1answer
170 views

Non-calculator proof that $\pi^\pi -\pi \lt \frac{100}{3}$

I am looking for a few non-computational, non-calculator proof of the following inequality: $$\pi^\pi -\pi \lt \frac{100}{3}$$ I can't really seem to come up with a proof because of that killer ...
4
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6answers
548 views

Proving $\pi^3 \gt 31$

$$\large \pi^3 \gt 31$$ Using a calculator, $\pi^3/31 \approx 1.0002$, so I thought this may be challenging to do by hand. It is extremely easy with the use of any calculator, so I was wondering ...
0
votes
0answers
7 views

How do I validate my ARMAX model?

Say I have some ouput $y_1, y_2, \ldots, y_N$ and inputs $x_1, x_2, \ldots, x_N$ which, by various time series methods, I've found to match an ARMAX(2,2,1) model. So I've found the estimations for ...
0
votes
0answers
17 views

Formula for MLM like system

I'm trying to figure out a formula for a system similar to a MLM system such that all members will receive 50/50 of the shares. So for example, X recieves 50% and A recieves 50%. When A recruits B and ...
0
votes
0answers
36 views

Inverse of sum of matrices

Let $A,B$ be invertible positive definite matrices of the same size. My goal is to efficiently compute $(xA + yB + zI)^{-1}$ for many triplets of positive real numbers $(x,y,z) \in \mathbb{R}^3$. ...
1
vote
1answer
78 views

Minimizing computations for evaluating two polynomial simultaneously

I want to evaluate two polynomials $f$ and $g$ simultaneously, on the same input (in a computer program). These polynomial have only coefficients $0, 1, a , b$ and their degree is less than 700. I ...
1
vote
1answer
67 views

Finite element method books

I know this question has been asked before; I just want to enquire if anybody has any suggestions to learn how to compute finite element problems, including plenty of examples. The topics I would ...
6
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2answers
96 views

For what values of $k$ does $(1+x)^{500+k}(1-x)^{500-k}$ exceed $10^9$?

Pretty simple question, for what values of $0\leq k \leq 500$ do we have $\max\{(1+x)^{500+k}(1-x)^{500-k}|x\in[0,1]\} \geq 10^9$ ? Some trivial observations: The problem is equivalent to finding ...
0
votes
1answer
37 views

More efficient method of computing the square root of $-1 \mod p$

I am currently doing collecting some preliminary data about elliptic curves over finite fields of order $p$ where $p$ is a prime congruent to 1 mod 4. Part of the data collection process requires me ...
-1
votes
1answer
29 views

c(x) = k for all positive k is primitive recursive [closed]

How can I show this function is whether primitive recursive or not? Do I need to use Godel number?
3
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0answers
55 views

Is there a systematic way of “discovering” an algebra from observations of its universe?

I am faced with the following situation: I have a finite set of some $m$ positive integers $Q^m \in \mathbb{N}$ These integers go through a series of $N$ possible black boxes that transform them. ...
0
votes
1answer
32 views

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 ...
0
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0answers
17 views

Solve Lotka-Volterra by hand? [duplicate]

I learn Lotka-Volterra model in computing mathematics textbook and solve it by different numerical methods. $$ \frac{1}{x}\frac{dx}{dt} = a - by$$ $$ \frac{1}{y}\frac{dy}{dt} = cx - d$$ where, ...
3
votes
2answers
91 views

Squeezing primes

Any positive odd number $n$ can be coded one binary digit smaller by the rule $\frac{n-1}{2}$ and that's obviously the best squeeze: a bijection from $\mathbb N$ such that $f(n)\geq n$. I'm looking ...
6
votes
3answers
103 views

Digits of $\pi$ using Integer Arithmetic

How can I compute the first few decimal digits of $\pi$ using only integer arithmetic? By 'integer arithmetic' I mean the operations of addition, subtraction, and multiplication with both operands as ...