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

learn more… | top users | synonyms

3
votes
2answers
266 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
347 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
126 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
308 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
127 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
79 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
154 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
86 views
5
votes
1answer
291 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
179 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
98 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
129 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
152 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
89 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
218 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
53 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
152 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
96 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
94 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
96 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
140 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
149 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
139 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
256 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
75 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
205 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
87 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
219 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: ...
23
votes
7answers
839 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
221 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 ...
53
votes
2answers
10k views

How can I use Mathematica's graph functions to cheat at Boggle?

Boggle is a word game played with 16 dice and a 4x4 tray. This question is inspired by a Stack Overflow question about Boggle that I decided to solve using Mathematica. In addition to Mathematica, I ...
8
votes
2answers
313 views

Recursive partitioning: Is there a better way to do this?

Consider the following function, which recursively splits a list into equal length sublists (the length of the list is assumed to be a power of the second argument): ...
0
votes
0answers
180 views

simulate a 32-bit signed integer overflow in a recurrence function

Considering the following recurring equation: which is this factorial function: I want to find the value of x where f(x) = 0. Actually, the solution is impossible with Mathematica, and it's ...
5
votes
2answers
595 views

Variable that changes itself

I am trying to store a boolean value into a variable with the additional property that the value changes each time the variable is called. ...