Questions tagged [iteration]
The iteration tag has no usage guidance.
151
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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 ...
- 243
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1
answer
80
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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
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2
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113
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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 $2\times2$ ...
- 481
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51
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Integration does not converge in iteration
I have the following code to find a numerical solution for a singular BVPas attached in the picture. I have the following Mathematica code: (This code of this question can be found at Mathematica does ...
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103
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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}
]
- 327
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98
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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}...
- 169
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64
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Solve two equation by fixed point iteration method
I am tryin to reproduce the figure.2 of this paper. In order to obtain this plot, I need to find the global minimum of equation.(7) or equivalently solving two coupled equations of $\frac{\partial \...
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119
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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 ...
- 169
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85
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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 ...
- 65
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49
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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+\...
- 169
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123
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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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247
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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 ...
- 1,043
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252
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Nested floor functions
I would like to compute a limit involving a particular nested floor function. For example:
...
- 67
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4
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317
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Defining a function iteratively without Mathematica getting stuck in a recursion loop
I have the following code:
...
- 618
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58
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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 ...
- 67
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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 ...
- 169
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1
answer
120
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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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49
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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 <...
- 137
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471
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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). ...
- 1,087
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95
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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 ...
- 849
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261
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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
...
- 755
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72
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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 ...
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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 ...
- 445
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49
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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 ...
- 723
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37
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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.
...
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36
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Force list of colours to have same grayscale value, maintaining hue
A sketch of what I'd like to achieve is given by
...
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513
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Best way to count nest depth in e.g. f[f[f[...[f[x]]...]?
What is the best way to count nesting depth in e.g. f[f[f[...[f[x]]...]? In other words, what function func is good for giving ...
- 611
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How to do simple list traversal? And how do I insert this in a function?
I want to make a function that takes as input a list of numbers and returns a list of 4 lists; the first returned list holds all positive real; the second returned list all negative real; the third ...
- 11
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134
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How to use NestList for coupled equations?
I have a code that works for a single equation. How to I use NestList for two equation that are coupled?
Below is the code for single equation,
...
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137
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Repeating and Sequencing Procedures with two Do-loops
I have a Do loop where I'm looking for the value of certain parameters that respect the conditions inside an If, and with those values, a run another Do to make another calculation of an expression ...
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118
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Using the Fold function with multiple parameter inputs [closed]
I want to construct something like: f[a, b, c, f[a, b, c, f[a, b, c, f[a, b, c, f[a, b, c, f[a, b, c, x]]]]]]. I believe this can be done using the Fold or Nest ...
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Iteration limit exceeded
I am trying to adapt the following piece of code (coming from this answer):
...
- 6,134
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How to use NestWhile to get it to work the way I want?
I have a vector th={0,0,...,1.57}. Now I want to choose the second element and change it by stepsize 0.2 until it is less than 1.57, I need these set of vectors:
th={0,0.2,0,...,1.57}
th={0,0.4,0,...,...
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Heat transfer with functions defined on different domains
I'm attempting to model a situation in which a polymer initially at a higher temperature is sandwiched between two cooler metallic mold pieces with conductive boundary conditions in between the ...
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How to recreate this complex iteration
I came across this image in a book Im reading:
(taken from Rational Iteration Complex Analytic Dynamical Systems from Steinmetz. I hope it is okay to share it here)
and I try to recreate it in ...
- 1,114
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NestList in 12.1/12.2 is 10x slower than 11.3/12.0
Are there any configurations to fix it?
Test code:
...
- 6,817
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FoldList and Compile [closed]
Let me elaborate my previous question about Foldlist and Composition.
...
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94
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FoldList with Composition and parameter
Good day to everyone!
I have two (just for simple example) functions and they compose a map:
...
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Generating a lattice by $𝑁^{𝑡ℎ}$ iteration of unit cell
This question is in continuation of the my previous question that was not clearly presented by me at all.
I have a unit cell, and I would like to generate a lattice but in iterative order.
For ...
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Functional iteration of list of functions
I'm getting completely stumped on writing a function makeIterate that constructs an iterated structure out of a list of functions e.g. ...
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How do I correctly iterate using Outer when an argument / slot is a nested list?
I have the following complex nested iteration situation.
I begin with a list, data, that comprises 16 TemporalData objects
Each TemporalData object contains 2 ...
- 105
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Why Mathematica doesn't compute the permutation products in my NestList[]?
I wrote the following:
K = DihedralGroup[5];
K = GroupGenerators[K];
y = K[[1]];
x = K[[1]];
l = NestList[PermutationProduct[x, y], x, 4]
But Mathematica gives me ...
- 4,801
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n-dimensional recursion [closed]
I am trying to set up a recursive function that generates n number of differential equations for Subscript[y, n][t]
This ...
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Iterative and recursive approach to generate Fibonacci sequence
I'm new to use Mathematica and using this demo project to understand Mathematic demo example.
I modified example code to only plot the runtime of recursive version of Fibonacci sequence runtime:
...
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Plotting iterates of a piecewise defined map
This is a follow up question to the one I asked here. I’ve succeeded in figuring out how to plot the first image of my piecewise defined transformation $T: [-1,1]^2 \to [-1,1]^2$, but now I want to ...
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Generating a $N^{th}$ iterative line graph from the adjacency matrix $M$. How to generate $M$?
I have a unit cell, and I would like to generate a lattice but in iterative order.
For instance, consider the following example--
The unit cell is (zero iteration)
This figure is generated by a ...
- 673
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How to write a function returning Chebyshev Polynominals of the first kind using Nest[]? [duplicate]
I want to create a function returning the Chebyshev polynomials of the first kind using the in build Nest[] function, preferably with a pure function.
I know there exist an in-build function for the ...
