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

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1answer
68 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 ...
-1
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0answers
19 views

Delete integer cases that contain specified number [duplicate]

I have a sequence generated with this RecurrenceTable function: RecurrenceTable[{a[n + 1] == 7 a[n], a[1] == 3}, a, {n, 1, 10}] and I would like to remove the ...
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0answers
25 views

Recursion with an exception [duplicate]

I need to print the first 7 members of the sequence a[n] with its reccurence formula a[n+1]=7*a[n]+n, where a[1]=1 and the digit 7 dosnt occur.
1
vote
1answer
325 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 ...
0
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0answers
66 views

Using Mathematica to solve a recursive system of differential equations

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
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2answers
40 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 ...
11
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2answers
263 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 ...
0
votes
2answers
73 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 ...
1
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1answer
61 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 ...
0
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1answer
66 views

Solving recursion equation with two parameters

I am trying to solve the following recursion equation, a(l,m)=l*a(l,m-1)+a(l-1,m) with initial condition; a(l,m)==0 if l=0 , a(l,m)==1 if m=1 I am trying to solve it ...
0
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0answers
54 views

Recursive computation using Piecewise

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 ...
2
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0answers
50 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 ...
6
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1answer
312 views

Speeding up the non-negativity algorithm for multilinear function with interval probabilities?

The algorithm is a branch-and-bound algorithm that calculates the non-negativity of a multilinear function with interval probabilities. The lines 9-11 has an optimization that is explained on the ...
0
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2answers
66 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 ...
0
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0answers
29 views

Does the two function for the same input leads to same output?

The first function is y[n_]:=x[n]+0.5*x[n-1]+0.25*x[n-2] the other is y[n_]:=a*x[n+1]+b*x[n]+c*x[n-1] Does exist some ...
0
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1answer
73 views
5
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1answer
190 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 ...
2
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1answer
114 views

Can Mathematica solve this type of recurrence?

I have the following recursively defined equation: ...
27
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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
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2answers
62 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 ...
2
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2answers
111 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
82 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
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0answers
35 views

Index change in a recursive definition

Assume I have the following recursive definition: ...
2
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1answer
53 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
2answers
71 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 ...
1
vote
1answer
89 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 ...
2
votes
1answer
67 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 ...
2
votes
1answer
48 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 + ...
2
votes
2answers
79 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 ...
2
votes
2answers
174 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
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1answer
46 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
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1answer
113 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
61 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: $$ C_N=N+1+\sum_{0≤k≤N-1}\frac{1}{N}(C_k+C_{N−k−1}) $$ ...
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1answer
40 views
0
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2answers
67 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 ...
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1answer
228 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
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1answer
41 views

Function to Represent Recursive Integral

I'd like to represent the following recursive integral equation to evaluate/graph (for $n\leq3$): $K_{i,n}\left(x\right)=\intop_{x}^{\infty}K_{i,n-1}\left(y\right)dy$ where ...
0
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2answers
54 views

Solving linear recursions without constant depth in mathematica

Mathematica does not like this recurrence relation. I do not understand why? ...
0
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1answer
84 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
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2answers
62 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
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1answer
76 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. ...
0
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2answers
273 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
106 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
71 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
84 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
177 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
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1answer
58 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: ...
0
votes
0answers
79 views

Simple recursive function?

I'm new in Mathematica and need some help. I'm trying to make a recursive function but I'm not sure how to iterate through more than one item. To be more clear, take this pseudo code for example: ...
11
votes
3answers
291 views

ToExpression fails with long nested string expressions

Consider the following conversion from String to Mathematica Expression: ...
1
vote
1answer
139 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 ...