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

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10
votes
4answers
268 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
460 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
0answers
92 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 ...
7
votes
2answers
368 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 ...
3
votes
1answer
331 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
594 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
117 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 ...
5
votes
1answer
661 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) = ...
42
votes
2answers
9k views

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

This question is inspired by a Stack Overflow question that I decided to solve using Mathematica. In addition to Mathematica, I thought I'd use some of the new version's graph-related functionality, ...
4
votes
3answers
282 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
167 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
252 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
211 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
3answers
541 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
296 views

Error Interpretation in NIntegrate

I am using a recursion algorithm developed by Migdal for Lattice Field Theory, and I have the following code: ...
9
votes
6answers
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
392 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 ...
1
vote
1answer
2k views

Defining a recursive sequence

I want to define a recursive sequence and then ask Mathematica to print a specific value: Am I doing something wrong?
0
votes
2answers
223 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 ...
5
votes
1answer
464 views

Solving recurrence relation using Mathematica defined in a piecewise way

I have a recurrence relation defined as following: RSolve[ { p[0] == p0, p[1] == λ p[0]/μ, p[i + 1] == λ p[i]/(2 μ) }, p[i], i ] Note that the relation ...
0
votes
1answer
383 views

How to solve a problem in relative motion?

I have a project due tomorrow that I have been struggling with for a month. I am utterly stumped, any help would be appreciated. The problem is: There is a ferris wheel, 30m in radius, set 80m ...
7
votes
1answer
267 views

Setting $RecursionLimit across all parallel kernels

I'm trying to optimize an elliptic curve factoring method by running it in parallel. There is a recursive step which required me to set the recursion limit higher than 256, however when I try and run ...
3
votes
1answer
200 views

Avoid crash in recursive Dynamic

With the following Dynamic cell, I can reproducibly crash Mathematica, so do not try this unless you have saved all your work! ...
1
vote
1answer
153 views

Differentiation w/o assiging concrete values

v = Subscript[v, 0]*Sin[(Pi*S)/Subscript[S, 0]]; a = dv/ds v; a = D[v, s] returns ...
33
votes
4answers
2k views

How can I implement dynamic programming for a function with more than one argument?

Dynamic programming is a technique for avoiding the repeated computation of the same values in a recursive program. Each value computed is immediately stored. If the value is needed again, it is ...