Questions tagged [recursion]
For questions about defining recursive functions, recursive algorithms and solving recursive equations.
655
questions
5
votes
2
answers
117
views
Building up a sequence dealing with a complex recursive scheme
Suppose I have multiple lists, the first one contains 2 elements, the next one 4 elements, the next one 8 elements, and so forth.
Let these elements be labeled as Gij where i refers to the list it ...
- 169
2
votes
1
answer
155
views
Recurrence relation for multivariate polynomials
I am trying to define a function which recursively computes a polynomial associated to every binary string:
ComputePoly[s_]:=(** Recurse on the string s**)
For ...
- 693
2
votes
2
answers
479
views
Why does Mathematica not evaluate the difference recurrence using `RSolve` or `RecurrenceTable`?
Mathematica does not evaluate the following recurrence of two variables using RSolve and only echoes the input:
...
- 840
9
votes
1
answer
599
views
What do RecursionLimit and IterationLimit actually set?
The following recursive functions respectively calculate the length of a Short-cut Collatz Conjecture series and perform a pointless demonstration recursion:
...
- 4,602
8
votes
4
answers
681
views
21
votes
4
answers
2k
views
How to define a recursive pattern?
I want to translate this recursive syntactic definition into a Mathematica pattern1:
$$
\mathtt{x}:
\begin{cases}
\text{Null}\\
\{\textit{integer}, \mathtt{x}\}
\end{cases}
$$
In other ...
- 11.7k
6
votes
1
answer
196
views
Closed form of two-layer recurrence
I am trying to find a closed-form expression for $A(0)$, described by the following recurrence forms, as a function of $L$ and $d$:
\begin{align}
A(\ell) &= 1 + 2^d A(\ell+1) + \sum_{g=0}^{d-1} \...
- 161
3
votes
1
answer
304
views
Kernel crashed after $RecursionLimit = Infinity
$RecursionLimit = Infinity;
T[n_, k_]:= T[n, k] = If[n == 0 || k == 1, 1, T[n, k-1] + If[n<k, 0, T[n-k, k]]];
Table[T[n!, n], {n, 1, 9}]
Without ...
- 2,949
2
votes
2
answers
157
views
How to build recursive function which only remembers every pth value and the last two values?
I need to create a recursive function of the natural numbers $f$ which only remembers the last two values it has found and every $p$th value. Below is the form of the code that I am working with, but ...
14
votes
3
answers
697
views
Mimic a procedural, recursive clustering algorithm for site percolation using functional programming
Sorry in advance for my logorrhea: I just want to make sure all of the information is here.
Context and Question
I am investigating site percolation on a square lattice. I have a working, depth-...
- 23.4k
3
votes
2
answers
2k
views
Import nested JSON file [duplicate]
For a project where I receive JSON messages from a web server I was trying to convert these messages into a format that can be used easily within Mathematica. Because JSON also consists of key-value ...
- 1,638
5
votes
2
answers
2k
views
Recursive Euclidean algorithm in Mathematica
Can anyone explain to me how do I use a recursion, if I don't know the limit? For example, I need the remainder $r$ of the Euclidean algorithm for $\gcd(a,b)$ which equals $0$. I figured out that the ...
- 199
0
votes
2
answers
144
views
Using Nest on a function that takes a function as one of its arguments [closed]
I have a function, nS[f_, xk_], which takes as arguments a function f and a vector xk. It ...
2
votes
0
answers
348
views
Using Mathematica to solve a recursive system of differential equations [closed]
I believe I have a difficult problem to work on specially because I don't have any previously experience using Mathematica in this kind of situation. So I'll try to describe it as best as I can hoping ...
- 113
2
votes
1
answer
404
views
Computing a recurrence table backward
I am trying to understand how to compute a recursive equation backward say n = 10 to n = 1. I am trying to solve a PDE for which ...
- 197
2
votes
1
answer
476
views
Usage of Piecewise/RSolve to solve an equation based on condition
I am trying to compute price of call option on a stock using the finite difference method. I have a VBA code for it, and I am trying to find out how I can use Mathematica memoization functions and ...
- 197
2
votes
0
answers
176
views
Recursive computation using Piecewise [closed]
I am trying to create an array using a series of equations using Piecewise. I am stuck in one of them. I am just putting a simplified version of code as below.
I ...
- 197
2
votes
2
answers
615
views
Find recurrence relation for a sum
Let's say I want to find a recursive equation for an exponentially weighted moving average
EV[t_]:=(a-1)/(a^t-1)*Sum[a^(t-i)*x[i],{i,1,t}]
I can do that manually ...
- 283
1
vote
1
answer
308
views
RSolve with integrations
I want to solve this question with Mathematica.
$$T_0(t)=c(t),\quad T_n(t)=a\int_0^t T_{n-1}(s)\, \mathrm{d}s+b(t).$$
Is it possible to solve $T_n(t)$ with RSolve?...
- 245
5
votes
0
answers
120
views
How to speed up solution of system of recurrence equations
I was wondering how I can improve the speed on this method for solving a particular system of coupled recurrence equations. The system is
$$
\begin{align*}
&V(m)=\alpha + \beta V(m+1)+\beta \sum_{...
- 637
1
vote
2
answers
733
views
Express recursion formula by Nest function
I'm fairly new to Mathematica and I have to express a formula by Mathematicas Nest-function. I'd like to find the solution for my formula by my own, thats why I ...
- 13
1
vote
1
answer
128
views
Calculating a function repetitively without using a For loop
In my programme I have defined all these functions:
...
- 193
3
votes
1
answer
222
views
Can Mathematica solve this type of recurrence?
I have the following recursively defined equation:
...
- 501
0
votes
2
answers
111
views
Writing a function with variable arguments [duplicate]
I want to write a function which takes multiple arguments varying from 1 to n, where each argument is a triplet.
sublistProduct[{$a_1,b_1,c_1$},{$a_2,b_2,c_2$},...] = { $\Pi_{i=1}^{i=n}a_i ,\Pi_{i=1}...
- 35
3
votes
2
answers
884
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How to create a recursive TreeGraph
How could I create a recursive tree graph, such as one defined by the following:
A family of trees $T_n$ are defined recursively as follows, for all integers $n \ge 1$.
The tree $T_1$ consists of a ...
- 215
2
votes
1
answer
172
views
How to solve for the closed form of this recurrence?
For integers $L,k \geq 0$:
$$T(L,k) = \begin{cases}
0 & \text{if }k \geq d, \text{ever}\\
-a_{k} & \text{if }L=0 \text{ and } k<d\\
a_dT(L-1,k+1) - a_{k}T(L-1,0)& \text{if } L>0 \...
- 155
6
votes
1
answer
782
views
Compile, "global variables" and recursion
I am trying to do something similar to this, namely to make a Compile'd function outer that itself calls a ...
- 6,805
1
vote
0
answers
115
views
2
votes
1
answer
87
views
Evaluate recursive funtion as a whole before computing a recursive step
I'll try to make a basic example of my problem with $n$ being an array of elements, ex. $\{1,2,2,3,3,3\}$:
If i have a sum which needs a computed value i would like to compute it beforehand and store ...
- 263
4
votes
2
answers
1k
views
Recursion problem
I try to make designation
a = {Subscript[a,1], Subscript[a,2], Subscript[a,3]}
but receive mistake
$RecursionLimit::reclim: Recursion depth of 1024 exceeded.
...
- 573
1
vote
1
answer
441
views
Iteration convergence of Newton approximations
I am trying to determine for which initial values Newton's approximation of specific functions (EX: f(x)=x^2 -1)converge and to what numbers it will converge to.
*Where Newton's approximations are x[...
- 193
2
votes
1
answer
256
views
Getting the first $n$ terms of a recursion relation
Given a recursion relation, I would like to generate the first $n$ terms (automatically) without having to go term by term.
Background
Each term is of the form $a_{n}(t)$, that is, $a_{n}$ is a ...
- 121
3
votes
1
answer
259
views
How do I make Mathematica nest argument changes?
I want something like Nest[f,x,n], but what where f is an argument change like a pushforward and x[t] is a function, for example, symbolically, and not in any sort of code:
$$
F{x[t]} \equiv x[2t + 1]...
- 33
7
votes
2
answers
1k
views
Finding large Collatz Sequences, trying to improve speed
Background: I am already very much in love with Mathematica but I am also a novice. So far I have only gathered experience in procedural programming in Python. Generally speaking I am trying to ...
- 195
3
votes
3
answers
697
views
Delay difference equation
How can I correctly specify and solve a system of delay difference equations in mathematica similar to NDSolve with regard to delay differential equations?
For example if I want to "see" the values ...
- 2,985
3
votes
1
answer
368
views
RSolve and a recurrence relation
In the book An Introduction to the Analysis of Algorithms there is a recurrence relation for the number of compares used in Quicksort algorithm:
$$ C_N=N+1+\sum_{0≤k≤N-1}\frac{1}{N}(C_k+C_{N−k−1}) $$
(...
- 65
4
votes
1
answer
207
views
How can I implement this recurrence equation in Mathematica?
I asked a similar question yesterday but today I realized that I was implementing the wrong function. I have tried changing the implementation but I can't get it to work.
Problem:
There is a river ...
- 107
0
votes
1
answer
80
views
Recurrence doesn't work together with maximize
When I'm trying to use a recurrence relation involving maximize it simply fails to compute anything...
...
2
votes
2
answers
447
views
How can I express this recurrence function in Mathematica?
\begin{equation}
r_{i+1}=r_{i}+V_{i}{\Delta}t
\end{equation}
Where
\begin{equation}
V_{i}=(0.01, 0.40)
\end{equation}
and ${\Delta}t$ is the difference in time.
My implementation (this is for ${\...
- 107
2
votes
1
answer
326
views
0
votes
2
answers
417
views
Help Solving A Recusive System: "$RecursionLimit::reclim: Recursion depth of 256 exceeded."
Was wondering if anyone had any tricks/ideas on solving this system of recursive equations I have. Essentially my goal is to have J2 equal to zero, but to understand how tweaking several parameters ...
- 265
-1
votes
1
answer
14k
views
Recursion depth of 1024 exceeded [closed]
I'm not sure why this code is giving the error :(
f[0] = 0;
f[n_] := f[n] = DigitCount[n, 10, 1] + f[n - 1];
f[1016]
- 633
3
votes
2
answers
374
views
Function to Represent Recursive Integral
I'd like to represent the following recursive integral equation to evaluate/graph (for $n\leq3$):
$$K_{i,n}\left(x\right)=\int_{x}^{\infty}K_{i,n-1}\left(y\right)dy$$
where
$$K_{i,0}\left(x\right)=...
- 133
0
votes
2
answers
71
views
Solving linear recursions without constant depth in mathematica
Mathematica does not like this recurrence relation. I do not understand why?
...
3
votes
2
answers
603
views
RSolve with conditional equation
I have the following conditional equation:
$f(n) = 1+2 f(n/2)$ when n is even
$f(n) = 1+f((n-1)/2)+f((n+1)/2)$ when n is odd
I want to represent this as a conditional equation to be used in ...
- 31
0
votes
2
answers
690
views
How to construct a linear feedback shift register
Are there any posts regarding the construction of a LFSR (Linear Feedback Shift Register) in Mathematica? I can't seem to find any and I am not sure how I would construct one.
- 143
0
votes
1
answer
127
views
How to improve this function that selects parameters from arbitrary distribution using Recursion?
Below, I have defined a function using Which to select model parameters based upon various conditions. My questions are: Is there any danger in writing this function using Recursion?
Is there a more ...
- 769
1
vote
2
answers
162
views
Solving Recurrence equation for n
I have a recurrence equation $t_n$ which is defined as
$$
t_n=2.5t_{n-1}-1.5t_{n-4},\qquad \text{for }n\geq5
$$
Where
$$
\begin{align}
t_1&=5\\
t_2&=10.5\\
t_3&=26.25\\
t_4&=62.625
\...
user25319
4
votes
1
answer
245
views
Modifying Game of Life code so that the lattice can be seeded with life forms
I want to modify Game of Life code so that the lattice can be seeded with one or two new life forms like:
...
- 43
0
votes
1
answer
195
views
Problem with recursion depth
I want to solve a problem where I need to compute the Euler-Lagrange equation. However I receive a recursion problem, and I don't understand why.
...
- 1