Questions tagged [iteration]
The iteration tag has no usage guidance.
173
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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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2
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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: ...
-1
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1
answer
91
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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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1
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46
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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 ...
- 21
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91
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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
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5
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731
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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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36
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function with parallel iterations
coprimesParallelIter[n_] := DistributeDefinitions[GCD];
ClearAll;
ParallelTable[If[GCD[i, n] == 1, i, Nothing], {i, 1, n - 1}] //
Flatten // DeleteCases[Nothing]
...
- 493
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0
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37
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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 ...
- 107
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3
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392
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0
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72
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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:
...
- 514
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3
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476
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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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104
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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 ...
- 43
-2
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1
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87
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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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111
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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 ...
1
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3
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86
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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 ...
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181
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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:...
- 989
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1
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41
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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 ...
- 113
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37
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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 $n$,...
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2
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97
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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
$$\...
- 83
3
votes
1
answer
54
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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.
...
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0
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55
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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 ...
- 35.2k
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100
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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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4
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312
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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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23
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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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1
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109
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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
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57
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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 ...
- 315
4
votes
1
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112
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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 ...
- 481
3
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2
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118
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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 $2\times2$ ...
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92
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3
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3
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107
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2
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1
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295
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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}
]
- 359
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1
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205
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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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148
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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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105
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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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61
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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+\...
- 161
3
votes
1
answer
134
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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 "...
- 315
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3
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286
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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 ...
- 1,317
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3
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266
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Nested floor functions
I would like to compute a limit involving a particular nested floor function. For example:
...
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4
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354
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Defining a function iteratively without Mathematica getting stuck in a recursion loop
I have the following code:
...
- 636
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3
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68
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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 ...
- 139
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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 ...
- 161
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178
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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 ...
- 383
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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
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2
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524
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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). ...
- 1,089
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2
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122
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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 ...
- 869
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2
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462
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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
...
- 973
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0
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82
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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 ...
- 109
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127
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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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75
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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 ...
- 883
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0
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41
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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.
...
- 107