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

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2
votes
2answers
99 views

Using RecurrenceTable index to call elements of a vector

I am having trouble doing something that seems straightforward. I have a recursive sequence that I would like to produce which looks as follows: ...
1
vote
1answer
150 views

Recursive function taking functions as arguments

I'm trying to implement Lie brackets and derivatives of nth order. For doing this, I've stumbled upon something I don't understand. Here is an illustration: First I define the functions: ...
2
votes
1answer
544 views

Recursion depth exceeded

Below is my code for numerical solving of PDE with Crank Nicolson scheme. ...
4
votes
3answers
189 views

Modify this code using Module and While

I have written a recursive function and would like to re-write the code using Module AND While to compare the timings. Here is my recursive function for f[n], where 6 n f[n] = f[n-1] + n! for n>0 and ...
1
vote
3answers
282 views

List of Tribonacci Polynomials with Mathematica? [duplicate]

I want to list top ten of Tribonacci polynomials. I have following algorithm, but it doesnt work. ...
4
votes
1answer
113 views

RSolve gives a Context::ssle error

I want to solve the following recurrence equation RSolve[{(k + 2) c[k + 2] q^(k + 1) - c[k] == 0}, c[k], k] During calculation in Mathematica I get this ...
1
vote
1answer
318 views

Finding n-th term of a sequence of functions

Lets say, I have the following series of functions, $f_1=a+1$ $f_2=a^2+2a+1$ $f_3=a^3+3a^2+3a+1$ Assume that $f_4, f_5,$ and $f_6$ are also known. However $f_n$ is not known as a function of $n$. ...
5
votes
3answers
546 views

Implementing the Farey sequence efficiently

There is of course the silly implementation: FareySequence[n_] := Union[Flatten[Table[j/i, {i, 1, n}, {j, 0, i}]]] However, there are numerous properties and ...
2
votes
0answers
98 views

RSolve and incomplete gamma function

I am interested in how Mathematica uses the incomplete gamma function to solve difference equations. For example, if we have this inhomogeneous, 2nd order equation and use ...
2
votes
2answers
101 views

Rising Recursion Relationships

Lets say I want to compute the following function in mathematica: $G[n,k]=G[n+1,k-1] + G[n+2,k-2]$ where I know that $G[n,0]=n$ and $G[n,1]=n^2$. So, for example, $G[3,2]=G[4,1]+G[5,0]=4^2+5$ or, ...
3
votes
0answers
320 views

Solving recursion relations using Mathematica

I want to solve the recursion relation given in equation 2.7(a/b) on page $6$ of this paper. (..the initial seed is $F_1 = G_1 = 1$ and the functions $\alpha$ and $\beta$ are defined on page $5$ in ...
3
votes
2answers
253 views

Nonlinear recurrence relation

I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{n−1})^3)} 3$$ Is there another way to get a formula for the nth term?
6
votes
1answer
248 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 ...
1
vote
1answer
171 views

Recursion evaluate Table power exceeded limit

I wrote 2 simple recursive functions for calculating the power of a table. pol3[Tb_List, n_Integer?Positive] := If[n == 1, Tb, Tb.pol3[Tb, n - 1]] and ...
5
votes
1answer
113 views

Recursion and safety of SetAttributes[Function, SequenceHold]

Compare the timings below ...
5
votes
2answers
228 views

Update a function avoiding infinite recursion

I am quite new to Mathematica and not completely familiar with functional programming. I am currently working with a function (call it foo) and wish to change its behaviour, for example, by adding 1 ...
24
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 ...
2
votes
2answers
948 views

How to define functions for a parameter-dependent recursive sequence

I am trying to generate a two variable recursive sequence For instance on Mathematica, I did z[1] := {1, 1} B := {{t, 1}, {-1, t}} z[n_, t_] := B.z[n - 1, t] ...
1
vote
1answer
140 views

Unwanted hold in recursive function

I have a function (let it be called f) that does something useful for me and I want to be able to apply it to the elements of a list regardless of their depth and keep the list structure. For example ...
2
votes
1answer
97 views

Notation not recursive enough?

My notation is not recursing enough. For example, Notation[W[a_ | b_] ⟹ foo[a_, b_]/foo[b_]] Notation[W[a__, b_ | c_] ⟹ W[a__ | c_]W[b_ | c_]] Then ...
3
votes
1answer
138 views

Using NestWhileList to determine smallest prime value in series

I have a function recursively defined as follows: $a_{n+1}-1=(a_n-1)\times lpf(a_n)$, whe $lpf(x)$ is the least prime factor of $x$. Now, given an initial value of $a_0$, I would like to find the ...
3
votes
1answer
162 views

How to make a simple tree yourself with defined distances for each generation?

I'm trying to make a function that generates a tree for spin spin analysis in spectroscopy. I though it would be pretty easy, but I'm totally stocked. The tree should look something like this: ...
17
votes
3answers
707 views

How to clear parts of a memoized function?

I have a function of two variables, e.g.: f[a_, b_] := f[a, b] = something f[a - 1, b - 1] etc With the above code I used the concept of memoization to speed up ...
2
votes
0answers
207 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. ...
3
votes
1answer
176 views

How can I get the general term of this recurrence equations?

Following is the recurrence relation: a[1] = 1; a[n_] := a[n - a[n - 1]] + 1 Array[a, 28] I tried to use RSolve, but it ...
0
votes
1answer
215 views

Creating Recursive Sequences

Quite a simple question, I reckon, however, even quite an extensive search hasn't helped me. I want to define a recursively defined sequence that starts with defined ...
1
vote
0answers
188 views

RSolve doesn't solve this recurrence equation

RSolve[{1 == b ((c k[t - 1]^a - k[t])/(c k[t]^a - k[t + 1])) c a k[t]^(a - 1), k[1] == b, k[3] == a}, k[t], t] I tried to read the documentation in Help ...
5
votes
4answers
257 views

Can the general term my recurrence equations be written with Floor or Mod?

I want to know the formula for the general term of the following recurrence system. I guess it can be written with Floor or Mod. ...
2
votes
2answers
647 views

defining recursively a function with multiple if conditions

I am trying to recursively define a function which satisfies the following system of equations and which depends on two parameters $n$ and $l$, $$ \begin{align} A(x, n, l) &= F[ A(x,n-1,l) ]\\ ...
4
votes
1answer
142 views

RecurrenceTable with vector

Mathematica can do a RecurrenceTable with a vector, here is a simple example: RecurrenceTable[{x[n + 1] == 2* x[n], x[0] == {1, 2, 3}}, x, {n, 3}] with output ...
10
votes
4answers
292 views

Order items by closest to the previous

I have a list of 2D points (a table, imagine the data of a parametric plot shuffled) I would like to join the points with a line that starts from one of them and always goes to the closest one. I ...
4
votes
1answer
518 views

How do I use RSolve to solve a system of recurrence relations?

I am trying to solve a system of recurrence relations as follows. ...
3
votes
1answer
821 views

Solve pair of recurrence relations

[Corrected equations and added simple example] Can you solve a system of (loosely) coupled recurrence relations like this in Mathematica somehow? ...
3
votes
0answers
94 views

An recurrence equation that can be solved in version 7 but not in version 8

A friend of mine showed me this code sample: RSolve[{a[n] == a[n - 5] + 1, Sequence @@ Table[a[i] == 1, {i, 5}]}, a[n], n] // Timing It's solved by version 7 in ...
1
vote
2answers
218 views

While-Loop Linear Projection

I'm would like to do a linear progression for a recursive relation of a consumption function. Combining my program skills and my sparse knowledge of mathematica, I was thinking about doing it in a ...
3
votes
1answer
351 views

How to implement Condition programmatically?

I am writing my own symbolic functions with custom symbolic properties. So often I wish to introduce some automatic simplifications or evaluations, which return the same head as it's argument. This ...
9
votes
1answer
672 views

Compiling a recursive formula

My question is related to computing what is called "invariant measure" for a particular well known fractal - the Sierpinski triangle. We have an array m of four two by two matrices, say ...
2
votes
2answers
123 views

Recursion doesn't happen any more or doesn't happen correctly if I store the recursive relationship in a variable first

I know the following code will form a recursion: Clear["Global`*"] u[i_, n_] := u[i - 1, n] + u[i, n - 1] u[0, n_] := n u[i_, 0] := i u[2, 2] (* => 8 *) But ...
10
votes
2answers
403 views

How to deduce a generator formula for a polynomial sequence?

Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule: $$ \begin{array}{l} p_1(x)=x \\ p_2(x)=2 x-x^2 \\ p_3(x)= x^3-3 x^2+3 x \\ p_4(x)=-x^4+4 x^3-6 x^2+4 x \\ p_5(x)= x^5-5 ...
5
votes
1answer
866 views

Polynomial Approximation from Chebyshev coefficients

I would like to expand a function $f(r)$ in the domain $[0,R]$, around the points $r =0$, and $r = R$ in the following manner $f(r = 0) = \Sigma_{i=0,i = even}^{imax} f_i (r/R)^i$ and $f(r = R) = ...
5
votes
1answer
256 views

Build recursion in parallel?

Problem Let's define a simple recursion. f[1] = 1; f[n_] := f[n] = f[n - 1]*n; If I evaluate f in parallel ...
4
votes
3answers
309 views

How to generate a recurrent sequence

How to generate this type of sequence? $$ f(n, x) = x f'(n-1, x) \hspace{2 mm}, f(0, x) = e^x$$ How do I evaluate it for numerical values for $x = 1$ or any number?
1
vote
1answer
171 views

Using different random values at each recursion step

I have the following code: ϕ[0] := π/4 ϕ[n_] := Exp[-n] ϕ[n - 1] + Sqrt[1 - Exp[-2 n]] M M = RandomVariate[NormalDistribution[0, 1]] For this recursion relation, ...
6
votes
5answers
259 views

How to nest my own “times” function to get powers

I have a "times" function. I'd like to create a power function using it. It should look like this for an 6th power: ...
9
votes
2answers
224 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 ...
7
votes
1answer
955 views

Efficient backtracking with Mathematica

Backtracking is a general algorithm for finding all (or some) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c ...
2
votes
3answers
612 views

Recursive function on list

Please consider the following: I have to deliver the weekly customer demand data on time. I can start to produce my products one week in advance. So I was thinking ...
4
votes
1answer
318 views

Error Interpretation in NIntegrate

I am using a recursion algorithm developed by Migdal for Lattice Field Theory, and I have the following code: ...
11
votes
7answers
2k views

Recursive function with if-statement

I am trying to represent the following function definition in Mathematica: $$\begin{align*} f(1)&=1 \\ f(2n)&= \begin{cases}f(n) & \text{if}\space n\equiv0\pmod{2} \\ 2f(n) & ...
6
votes
0answers
416 views

Increasing recursion speed in Hull-White trinomial tree calculation

First timer here and have been finding these boards very useful in learning Mathematica. I'm trying to implement a numerical procedure for the Hull-White trinomial tree in Mathematica. Despite using ...