# Questions tagged [iteration]

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### How to obtain a solution to a system of equations using the method of successive approximations? [closed]

My question is not offtopic at all! It's about problem of syntax in Mathematica. It is necessary to obtain an analytical solution to a system of equations using the method of successive approximations ...
46 views

### How to fix parameter locally for iterating recursion equations

The following is a simplified version of a more detailed problem. I have two coupled recursion equations of two variables, x and y. One equation also depends on a parameter, c: ...
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### How to use functional iteration with changing function?

I recently came across this problem on reddit. The problem is supposed to be read like a snake, and the result of each succesive operation is sent to the next operation: There are 9 blank boxes and ...
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1 vote
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### Use Mathematica to Implement Blahut–Arimoto Algorithm (Part: Algorithm for Rate-Distortion)

Try to use Mathematica to implement Blahut–Arimoto algorithm (here we just focus on the part of computation of Rate-Distortion). Here are some reference code snippets: Python The algorithm looks ...
• 1,683
1 vote
105 views

### Use Mathematica to Implement Blahut–Arimoto Algorithm (Part: Algorithm for Channel Capacity)

Try to use Mathematica to implement Blahut–Arimoto algorithm (here we just focus on the part of computation of channel capacity) Here are some reference code snippets: MATLAB(a) MATLAB(b) Python The ...
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45 views

### Ising Model Simulation Increase Efficiency

I implemented a 2d simulation of Ising Model for zero external magnetic field. Below you can find the function I wrote to calculate the energy (periodic conditions) ...
150 views

### How to Optimize Integro-Differential Equation Solving Time in Mathematica?

I'm trying to solve an integro-differential equation numerically in Mathematica that models the evolution of a physical system . However, the computation takes a very long time and doesn't yield a ...
237 views

### Given two functions, generate all nested applications of the functions to a given order

I have two functions $f$ and $g$. Given some order parameter $n$, I want to created all nested applications of $f$ and $g$ and save them in a list. For example, for order 1 we will have ...
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398 views

### Reproduce the annulus fractal

I've made some attempts, but I don't know how to set the color and thickness of the circle. ...
• 243
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### Problem designing test for NestWhile?

I am trying to use NestWhile with a custom test as follows: ...
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216 views

### How to reuse an iterator in different functions?

How can I reuse iterators? For example, instead of Table[i, {i,0,10}] Table[i^2, {i,0,10}] Table[f[i], {i,0,10}] write something like ...
96 views

### Speed up multiple Do loop

I am writing a script to simulate the multi spin system and for that I need to use three successive iterations. The code runs fine but takes a long time. I need the final FID. So, has there a way to ...
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### How to find clear solution for iterative problem by condition $<v_k ,v_n>=0$ If $k!=n$

I want to find x[n] by v[n] values without x[n] in solution by iterative below problem: <...
1 vote
80 views

### Can't use iterative variable as part specification [closed]

I've got the following mathematica code: ...
47 views

### FindMinimum with many Sums and NIntegrates is very slow

I want to calculate the global minimum of an equation which has several hundred Sums (I used 300 in this code), but the calculation is very slow. My code is as ...
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1 vote
102 views

### Listing iterations inside a while loop

I wrote a code for bisection method root approximation. However, I wanted to know the value of the root every iteration. I tried using the Union function to save each iterated value in a set but it ...
• 43
133 views

### Exponential and logarithmic functions slow the higher iterations in Mathematica

I want to solve BVP given in the (39)-(40) by the method given below these equations. I have written this method in Mathematica as follows. However, for n=1 it print the solution quickly but for ...
64 views

### A geometric application of Benford's law [duplicate]

I would like some help solving the following problem using Mathematica: Show that, no matter what the initial area of an equilateral triangle is, the sequence of areas (painted in black) of the ...
1 vote
125 views

### A way to generalize my code for this non linear ODE problem

I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ using "Fixed Point Iteration" over the interval $[0,1].$ Now using central difference method I arrived at the ...
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1 vote
113 views

### Extend the code for more variables (at least 100)

I have this code (not in best shape) for a problem in 3 variables. It does the job. The problem is I want to extend this to more number of variables around 100 at least. It is very painful to extend ...
• 219
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### How can I count iterations with NestWhile?

I'd like to count loop iterations for some substitution rules. For example: rule = {1 -> {0}, 0 -> {1}} init = {0} maxIter = 10 I'm going to avoid all ...
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### Nested radical implementation

I am attempting to code $$F(x,n)=\sqrt{x+\sqrt{x+2\sqrt{x+\cdots +n\sqrt{x}}}}.$$ For example, $$F(x,1)=\sqrt{x+\sqrt x},$$ $$F(x,2)=\sqrt{x+\sqrt{x+2\sqrt x}},$$ and so on. I found the ...
66 views

### Successive multiplications using Mathematica tools

Successive rotations on the unit circle Given an arbitrary starting point $z$ on the unit circle in the complex plane, the goal is to compute a cycle of rotations by $\pi$/2 with successive ...
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68 views

### How to make faster of a code containing more iteration point? [closed]

I am trying to evaluate a code of the Power Series Solution method to get the results. Also, the time of evaluation depends on the parameters I am using. When the iteration point is 50, 60, or 80, it ...
79 views

### Sequence of lists

Let's say I have the following table, y=40; b=Flatten[Table[{i, j}, {i, 1, 2.25, 1.25}, {j, y - 5, y - 8, -3}], 1] then c is equal to, ...
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### Question regarding initial guesses for Newton's method in AceGen/ AceFEM

I am trying to solve a system of equations with the command SMTNewtonIteration[]. This method needs initial guesses for the degrees of freedom I am looking for. Is ...
1 vote
116 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 ...
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### 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: ...
104 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. ...
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### 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 ...
105 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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### 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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43 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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### Better way to do such iteration

Consider such an iteration function ...
• 7,148
1 vote
518 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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### 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 ...
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122 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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### 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 ...
131 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 ...
246 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
51 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 ...
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### 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 $n$,...
• 101
1 vote
106 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 \...
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### 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. ...
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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### 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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349 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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### 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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