For questions about defining recursive functions, recursive algorithms and solving recursive equations.

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14
votes
3answers
340 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-...
6
votes
1answer
126 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} \...
2
votes
1answer
114 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
votes
2answers
72 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 ...
3
votes
2answers
274 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 ...
2
votes
1answer
63 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 ...
2
votes
1answer
349 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 ...
1
vote
0answers
127 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 ...
0
votes
2answers
46 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 ...
12
votes
2answers
313 views

Can RecurrenceTable make use of CompiledFunction?

I'm trying to implement a discrete-time 2D Verlet algorithm for a point-mass subject to a softened gravitational interaction as a test for a more computationally intensive simulation using ...
2
votes
1answer
130 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 ...
3
votes
0answers
80 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_{...
1
vote
2answers
157 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 ...
1
vote
1answer
91 views
5
votes
1answer
303 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 ...
3
votes
1answer
143 views
29
votes
4answers
1k views

What tools can help in realizing tail recursion?

I had nice discussions with Leonid and Rojo that got me interested in tail recursion. Tail recursion is not always easy to realize with Mathematica, so it would be nice to have some tools to help with ...
0
votes
2answers
83 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}...
3
votes
2answers
180 views

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 ...
2
votes
1answer
99 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 \...
1
vote
0answers
51 views

Index change in a recursive definition

Assume I have the following recursive definition: ...
2
votes
2answers
133 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....
1
vote
1answer
155 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[...
2
votes
1answer
110 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 ...
3
votes
1answer
94 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]...
2
votes
2answers
219 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 ${\...
0
votes
1answer
54 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... ...
4
votes
1answer
154 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 ...
2
votes
1answer
97 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: $$ C_N=N+1+\sum_{0≤k≤N-1}\frac{1}{N}(C_k+C_{N−k−1}) $$ (...
1
vote
1answer
56 views
0
votes
2answers
98 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 ...
-2
votes
1answer
3k 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]
0
votes
2answers
57 views

Solving linear recursions without constant depth in mathematica

Mathematica does not like this recurrence relation. I do not understand why? ...
0
votes
1answer
97 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 ...
1
vote
2answers
78 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 \...
0
votes
1answer
91 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
vote
2answers
301 views

Recursion on a moving window

I need to apply some computations to a moving window of $N$ items in a time series and I am struggling with doing recursion and shifting the considered window. To illustrate, please consider the ...
4
votes
1answer
143 views

Display level of recursion of a recursive function during execution

Given a recursive function, is there some simple way to display or store the value of recursion or "how many levels deep" the function is at a given time? For instance, if we wrote the recursive ...
0
votes
1answer
150 views

Recursive definition of nested sums

I have a set of functions which take lists as arguments. They recursively nest sums, and I have defined them as follows ...
1
vote
1answer
141 views

How to rewrite and possibly speed up a recursive sum?

I have the following for-loop calculating a multiple nested sum ...
1
vote
1answer
259 views

Define a Recurrence Table involving other tables

I'm relatively new to using Mathematica. Previously I used Matlab, but lately I noticed that the numbers i got in both of them do not match (mostly it seems that Matlab lacks precision...). The ...
1
vote
1answer
76 views

Implementation of a recursive function [duplicate]

I have been trying to implement a recursive function, but still struggle. Here's what I have written: ...
1
vote
1answer
172 views

how to make a recursive function to analyse this file

I am stuck at this problem beginning We assume we have keyword k, and the structure in the file: file.txt ...
1
vote
0answers
65 views

Problem with converting recursive code to iterative

I am trying to convert a snippet that uses recursion into one that uses iteration for drawing an L-tree, but my code produces duplicate points. How do I avoid generating them? Recursive version: <...
3
votes
3answers
206 views

Pare down list recursively

What is the best way to pare down a list whereby the $n$th number is removed from the list recursively? This ...
0
votes
1answer
88 views

How to define y[n] = f1 y[n-1] + u[n]?

I need to define a recursion defined by the following equation $y(n) = f_1 y(n-1) + u(n)$ In which $f_1$ is a symbolic constant. I know the values of the sequence u and I know the initial value of y....
2
votes
2answers
178 views

Understanding `NestList` with multiple functions

General question For a function f[n, a], where a is a list and n is a whole number, what is ...
3
votes
1answer
238 views

Mathematica taking too long to calculate recursive function

I have been trying to plot those specific recursively defined functions p1 and q1 in Mathematica: ...
24
votes
7answers
845 views

Alternative ways to implement a triangular recursion

Triangular recursions are a class of algorithms that frequently turn up in computational mathematics. These recursions are expressible in the general form $$T_k^{(n)}=f(T_{k-1}^{(n)},T_{k-1}^{(n+1)})$...
1
vote
1answer
226 views

Recursive functions taking list arguments

I wish to create a function that takes lists (e.g. {plus,plus,minus,0,minus,plus}) and uses the input list to calculate a corresponding value using a set of ...