Questions tagged [iteration]

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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: <...
user68119's user avatar
1 vote
2 answers
71 views

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

I've got the following mathematica code: ...
Sebastian 's user avatar
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0 answers
43 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 ...
user43830's user avatar
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1 vote
3 answers
93 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 ...
Mule's user avatar
  • 43
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1 answer
123 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 ...
Junaid Ahmad's user avatar
0 votes
0 answers
63 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 ...
Rubens Vilhena Fonseca's user avatar
1 vote
1 answer
93 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 ...
Learner's user avatar
  • 219
1 vote
1 answer
108 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 ...
Learner's user avatar
  • 219
2 votes
1 answer
128 views

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 ...
lesobrod's user avatar
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2 votes
2 answers
128 views

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 ...
Aaron Hendrickson's user avatar
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0 answers
65 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 ...
dantopa's user avatar
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-2 votes
1 answer
66 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 ...
supragyan priyadarshinee's user avatar
2 votes
1 answer
77 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, ...
a019's user avatar
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1 answer
79 views

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 ...
user1234321's user avatar
1 vote
1 answer
96 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 ...
Math_student's user avatar
2 votes
2 answers
232 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: ...
CuriousDudeFromEgypt's user avatar
-1 votes
1 answer
100 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. ...
Dylan Levine's user avatar
2 votes
1 answer
59 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 ...
Junaid Ahmad's user avatar
5 votes
1 answer
99 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, ...
rani's user avatar
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8 votes
5 answers
805 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 ...
expression's user avatar
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1 answer
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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] ...
Jamie M's user avatar
  • 493
3 votes
3 answers
406 views

Better way to do such iteration

Consider such an iteration function ...
matrix42's user avatar
  • 6,774
0 votes
0 answers
103 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: ...
Charmbracelet's user avatar
1 vote
3 answers
503 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?
boii's user avatar
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-2 votes
2 answers
135 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 ...
boii's user avatar
  • 43
-2 votes
1 answer
108 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: ...
boii's user avatar
  • 43
0 votes
1 answer
116 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 ...
Süleyman Küçük's user avatar
2 votes
3 answers
112 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 ...
Junaid Ahmad's user avatar
0 votes
1 answer
215 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:...
Vangsnes's user avatar
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1 vote
1 answer
47 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 ...
user122916's user avatar
0 votes
0 answers
48 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 $n$,...
Dan1618's user avatar
  • 101
1 vote
2 answers
102 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 $$\...
epselonzero's user avatar
3 votes
1 answer
66 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. ...
Чорны Бусел's user avatar
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 ...
rhermans's user avatar
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0 votes
1 answer
146 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 ...
licheng's user avatar
  • 2,005
6 votes
4 answers
331 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, ...
Aschoolar's user avatar
  • 883
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: {&...
lesobrod's user avatar
  • 1,197
3 votes
1 answer
131 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 ...
Nandan's user avatar
  • 61
1 vote
1 answer
69 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 ...
Eldar Sultanow's user avatar
4 votes
1 answer
158 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 ...
Jorge Castaño's user avatar
3 votes
2 answers
127 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 $2\times2$ ...
Jorge Castaño's user avatar
1 vote
2 answers
93 views

Using Loop to find a specific Energy

I am given a Hamiltonian: ...
codebpr's user avatar
  • 899
3 votes
3 answers
113 views

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

This code ...
Rogo's user avatar
  • 790
2 votes
1 answer
358 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} ]
user236343's user avatar
0 votes
1 answer
304 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}...
Junaid's user avatar
  • 161
0 votes
1 answer
155 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 ...
Junaid's user avatar
  • 161
0 votes
1 answer
110 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 ...
J0ta's user avatar
  • 65
0 votes
0 answers
69 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+\...
Junaid's user avatar
  • 161
3 votes
1 answer
145 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 "...
S.V's user avatar
  • 315
5 votes
3 answers
321 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 ...
Patrick.B's user avatar
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