Questions tagged [iteration]

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1 answer
84 views

How to find the minimum at each iteration?

I would like to iterate the table for {Q,0,3,1}, {R0,1,5,1}, the values of m=[3.83171, 7.01559, 10.1735, 13.3237, 16.4706, 19.6159, 22.7601, 25.9037] and calculate the corresponding k and Ra. Also, I ...
2 votes
2 answers
213 views

Solve can’t solve this… is there a way to approximate it?

I've been toying around with mortgage/loan calculations and spreadsheeting. The loan formula is as follows: A = p * r *(1+r)^n / ((1+r)^n - 1) A: payment per period p: principal r: interest rate n: ...
-1 votes
1 answer
91 views

Wolfram Alpha simplifying $\sqrt{1+x^\sqrt{1+x^\sqrt{1+...}}}$ incorrectly [closed]

I am pretty new to Wolfram Alpha. I want Wolfram Alpha to find the derivative of $\sqrt{1+x^\sqrt{1+x^\sqrt{1+...}}}$. At the moment, I am having trouble with Wolfram Alpha simplifying it incorrectly. ...
1 vote
1 answer
46 views

CPU time in iteration process

Let $Tx=\frac{x}{2}$ for all $x\in[0,1]$. Let $x_{0}\in[0,1]$ and set an iterative sequence $\{x_{n}\}$ by the method $x_{n+1}=Tx_{n}$. Now if $x_{0}=0.8$, then I get a convergent sequence towards the ...
5 votes
1 answer
91 views

List operation for beginner Usage of #1 and #2 (in stead of using for loop)

I have trouble using list operation of #1 and #2. Could you please tell me how to make it? I prepared the list as below, ...
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8 votes
5 answers
731 views

Create a regular polygon with n vertices given two points

I want to create a regular polygon from the initial two points $A$, $B$ and number of vertices $n$, regularPolygon[{0, 0}, {1, 0}, 3] gives ...
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0 votes
1 answer
36 views

function with parallel iterations

coprimesParallelIter[n_] := DistributeDefinitions[GCD]; ClearAll; ParallelTable[If[GCD[i, n] == 1, i, Nothing], {i, 1, n - 1}] // Flatten // DeleteCases[Nothing] ...
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0 votes
0 answers
37 views

Mathematica script not running properly on remote server

I am trying to run a mathmatica script on an hpc. First I converted the .nb into a .m file and changed the cell properties to initialization. But I am getting several errors while submitting the job ...
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3 votes
3 answers
392 views

Better way to do such iteration

Consider such an iteration function ...
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0 votes
0 answers
72 views

Implement of Euler Method of Parabolic PDE

I'm experimenting with different schemes for numerically solving PDEs in Mathematica. I use NestList to implement the Euler Method for 1-D PDE, the code is concise: ...
1 vote
3 answers
476 views

How to plot an imaginary number, i, power tower as done in the following way?

Can somebody explain what two variables exactly they have plotted against each other to get such graphs, and how one would go about getting this graph in Mathematica?
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-2 votes
2 answers
104 views

How do I create cobweb iterations or stair steps **WITH ARROWS** to show attractive and repulsive fixed points for a graph? [closed]

I'm new to Mathematica, so I would appreciate any help. How do I create cobweb iterations or stair steps WITH ARROWS to show attractive and repulsive fixed points for this graph? I want it to look ...
  • 43
-2 votes
1 answer
87 views

How to plot an iterative function of y(n+1) against y(n) in order to analyze the convergence of real power towers? [closed]

I'm new to mathematica and was wondering how to plot an iterative graph for power towers. If there is a power tower y= x^x^x^x^x^x^... we can rewrite it as an iterative equation in the following way: ...
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0 votes
1 answer
111 views

How can I nest a complex function?

I am examining the mandelbrot set so I need to iterate the function f[z_Complex, c_] := (z)^2 + c Besides, I want to choose the complex numbers dynamically from ...
1 vote
3 answers
86 views

Iterative method for fixed point of a mapping with domain and range contained in $\mathbb{R}^{2}$

Let $X$ be a metric space and $T:X\rightarrow X$ be a function. A point $x\in X$ is called a fixed point of $T$ if $x=Tx$. For example, if $X=[0,1]$ and $Tx=\frac{x}{2}$ then $T$ has a unique fixed ...
0 votes
1 answer
181 views

How to do a Picard iteration on a Volterra equation? [closed]

I want to approximate the solution of a Volterra integral equation using the Picard method, and plot the approximated solutions. For this I have the equation: where the functions and coefficients are:...
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1 vote
1 answer
41 views

How can I define an operator and plot its iterates?

I am trying to define a function (an operator) that "integrates then translates" a function. More specifically, for an input f[x], I want to integrate it as \int_0^x f[t] dt, then translate ...
0 votes
0 answers
37 views

Iterating an operator on a polynomial

I want to be able to build an operator $S$, on a polynomial in multiple variables which does something like this $f[x,y] =$ some polynomial $S[f][x,y] = y*f[y,x]$ And then for a specific choice of $n$,...
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1 vote
2 answers
97 views

Nested pure function argument as table

I made a nested pure function Nest[(x^2)/ ((2x+1) + #)&, x,n] I would like that for each iteration the value of x increment of 1, to have something like $$\...
3 votes
1 answer
54 views

NestWhileList stop criteria for second appearecnce of element

How i can stop evaluation of NestWhileList after second zero occurs? In my variant it stops at the first step. ...
2 votes
0 answers
55 views

Recursively create Graph from seed and Nest GraphUnion, keeping VertexStyle, EdgeLabels, VertexCoordinates, EdgeShapeFunction

TL;DR; GraphUnion does not preserve properties of the input Graphs. How do I combine two ...
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0 votes
1 answer
100 views

How to find a specific spanning subgraph?

A spanning subgraph is a subgraph that contains all the vertices of the original graph. Given a graph $G$, I would like to write a function $f$ for finding a spanning 5-regular bipartite connected ...
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6 votes
4 answers
312 views

Using multiple hashtags in NestList

Are multiple hashtags allowed in NestList usage? If yes, how to implement it? Example, f[{x_, y_}] := {x + y, x - y}; NestList[f, {100, 75}, 5] My attempt, ...
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0 votes
0 answers
23 views

Difference between SubstitutionSystem and StringReplace

I'm examining two-step substitution model: First step, division: {"A" -> "BC", "B" -> "AC", "C" -> "AB"} Second step, merging: {&...
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3 votes
1 answer
109 views

Iterative simultaneous numerical optimization of two functions

p = y 10 - 2 x^2 + 5 x; q = 20 y x - y^2 + 2 x; I want to maximize both functions simultaneously (Maximise p to get x and Maximise q to get y). I know that I could ...
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1 vote
1 answer
57 views

How do I construct and plot functions properly using NestList?

I am trying to construct a function using NestList and plot the values. Although the individually used and defined functions in my notebook seem to do the right ...
4 votes
1 answer
112 views

Two variable recursive integral equation

I'm trying to improve the question posted in Solving an integral vectorial equation by iterations but when the iterations are for two variables. I mean, suposse that I have the following integral ...
3 votes
2 answers
118 views

Solving an integral vectorial equation by iterations

I'm triying to solve a problem like the following: $$ \binom{f(t)}{g(t)}=\binom{f_0(t)}{g_0(t)}+\lambda\int_0^t ds\hat{A}(s)\binom{f(s)}{g(s)}, $$ where $f_0(t),g_0(t)$ and $\hat{A}(t)$ (a $2\times2$ ...
1 vote
2 answers
92 views

Using Loop to find a specific Energy

I am given a Hamiltonian: ...
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3 votes
3 answers
107 views

I need to create a series of polygons from a list of lists that form a stair step shape

This code ...
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2 votes
1 answer
295 views

What's a functional alternative to nested Do loops?

How can I use functional code to achieve the same effect as the following procedural code Do[ Do[ f[i,j], {j,1,m} ], {i,1,n} ]
0 votes
1 answer
205 views

Plotting fractals in Mathematica for S iteration

Dears, I'm trying to plot the attached picture figures in Mathematica software. Let $T(z)=z-\frac{P(z)}{P^{\prime}(z)}$. The S iterative scheme is for $z_{0}$ a starting point and $y_{n}=(1-\beta_{n}...
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0 votes
1 answer
148 views

Mathematica does not show anything after running for higher iterations

Consider a BVP: $y^{\prime\prime}=\frac{3}{2}y(t)^{2}$ with the boundary conditions $y(0)=4$ and $y(1)=1$. The exact solution is $y(t)=\frac{4}{(1+t)^{2}}$ and the initial guess is $y(t)=4-3t$. Now I ...
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0 votes
1 answer
105 views

Implementing While loop in module that will iterate correctly

I am attempting to write a module that prints an optimal path from a starting node to a destination node. The first node is 1 and the final node is 100 (though when module prints these they should be ...
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0 votes
0 answers
61 views

Solving numerically Pdes and Odes and Iteration processes

Dears, I have the following equations: $x^{\prime\prime}(t)=\frac{3}{2}x(t)^{2}$ with $x(0)=4$ and $x(1)=1$. The exact solution is $x(t)=\frac{4}{(1+t)^{2}}$. Now the corresponding operator is $ Px=x+\...
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3 votes
1 answer
134 views

FixedPoint not working, despite quick convergence of sequence [closed]

Trying the computation below, with Mathematica 13.0.0, I am not getting a result returned. FixedPoint[Cos, 0.85] This appears in the 3rd edition of "...
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5 votes
3 answers
286 views

ParallelDo barely faster than Do

I am new to parallel computing, so I am trying to get a grasp as to how this works. Many posts seem to indicate that overhead (like here) is a common pitfall, but I do not see why this would be the ...
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2 votes
3 answers
266 views

Nested floor functions

I would like to compute a limit involving a particular nested floor function. For example: ...
3 votes
4 answers
354 views

Defining a function iteratively without Mathematica getting stuck in a recursion loop

I have the following code: ...
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1 vote
3 answers
68 views

Digits product and an iteration process

I would like to create a code which gives me the square of the product of the digits of a number, with the only rule that if a number has a 0, then it doesn't count in the product (for example, if the ...
0 votes
1 answer
182 views

I'm beginner and do not how to plot the Basins of attraction by the methods

For a complex polynomial $P(z)$, define $T$ by $T(z)=z-\frac{P(z)}{P^{\prime}(z)}$, where $P^{\prime}(z)$ is the first derivative of $P(z)$. We consider Newton method for finding the roots of ...
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0 votes
1 answer
178 views

How to use for loop in Mathematica?

in most of my job I have to repeat something for different part of data, for example making plot, usually the only thing need to change is index. Below is the example of the code which I have to ...
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1 vote
1 answer
62 views

Why each iteration takes longer than previous one when using VariationalD in this loop?

I have a function $f$, and I would like to modify it iteratively to approach another one called $a$ (not because I think this is the best way to do anything, but for experimentation). For this, I use <...
10 votes
2 answers
524 views

What is the most efficient way to define a Loop until function?

Mathematica has the While function which is very convenient when we need to process some code until the attainment of a certain state (identified with a condition). ...
0 votes
2 answers
122 views

Spurious renaming in nested Function construct

From the documentation of Function, I take this example (slightly simplified). Renaming the dummy or bound variable (y->y$ in the inner ...
5 votes
2 answers
462 views

Replacing elements at a single level in a nested list

I want to replace all instances of 0 in the outer most level of a nested list with 1. However, when I use ReplaceAll as ...
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0 votes
0 answers
82 views

FindRoot doesn't find root

I am facing a problem that my FindRoot doesn't find the actual roots. I am trying to make a loop that iterates my parameter sets (U0,X0,\Sigma0) to find sets that satisfy some conditions. Here is my ...
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0 votes
0 answers
127 views

The use of `NestList `

After read Michael answer, code use NestList to compute and feed in numerical integration. I want to learn this idea into my code. In the ...
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0 votes
0 answers
75 views

Converting 1D map into first order differential equation for bifurcation diagram code

I have existing code to plot bifurcation diagram for coupled first order differential equations. It seems to work for coupled differential equations. To test the code further, I use the simplest ...
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0 votes
0 answers
41 views

Flatten a pair of matrices within a list of matrices

I have a list of matrices, which I think is better to give an example using the code. ...