For questions about defining recursive functions, recursive algorithms and solving recursive equations (e.g, with `RSolve`)
2
votes
1answer
68 views
Recursion depth exceeded
Below is my code for numerical solving of PDE with Crank Nicolson scheme.
...
4
votes
3answers
91 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 ...
0
votes
3answers
102 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.
...
5
votes
1answer
71 views
4
votes
1answer
87 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 ...
3
votes
3answers
216 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
42 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
66 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
111 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 ...
11
votes
2answers
600 views
How can I solve a difference-differential equation?
How do I ask Mathematica to try to solve a recursive relation that defines a sequence of functions? For example, suppose I know that $g_n(x) = g_{n-1}'(x)$ for $n > 0$ and that $g_0(x) = e^{2x}$. ...
2
votes
0answers
75 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?
4
votes
0answers
95 views
Speeding up multilinear PRA branch-and-bound algorithm with worst-case exponential time scenario with respect to basic events
The algorithm is a branch-and-bound algorithm that calculates dominances for PRA, probalistic risk assessment. The task was to find faster ways to do it in numerical software such as Matlab but we ...
1
vote
1answer
69 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
...
3
votes
1answer
446 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?
...
20
votes
4answers
543 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 ...
4
votes
2answers
114 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 ...
2
votes
2answers
232 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
81 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
71 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
78 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
102 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:
...
12
votes
3answers
297 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
106 views
Am I entering this 2-variable recurrence correctly?
I'm trying to solve this recurrence with two variables.
...
1
vote
2answers
166 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 ...
2
votes
1answer
107 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 ...
5
votes
1answer
167 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
...
0
votes
1answer
102 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
109 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
179 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
238 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 $l$,
$$
\begin{align}
A(x, n, l) &= F[ A(x,n-1,l) ]\\
...
3
votes
1answer
84 views
RecurrenceTable with vector
Mathematica can do a RecurrenceTable with a vector, here is a simple example:
RecurrenceTable[{x[n + 1] == 2* x[n], x[0] == {1, 2, 3}}, x, {n, 3}]
with output
...
8
votes
4answers
178 views
Order items by closest to the previous
I have a list of 2D points (a table, imagine the data of a parametric plot shuffled)
I would like to join the points with a line that starts from one of them and always goes to the closest one.
I ...
4
votes
1answer
242 views
How do I use RSolve to solve a system of recurrence relations?
I am trying to solve a system of recurrence relations as follows.
...
3
votes
0answers
75 views
An recurrence equation that can be solved in version 7 but not in version 8
A friend of mine showed me this code sample:
RSolve[{a[n] == a[n - 5] + 1, Sequence @@ Table[a[i] == 1, {i, 5}]}, a[n], n] // Timing
It's solved by version 7 in ...
5
votes
3answers
439 views
recursive integration
I am trying to do multiple integrations recursively. For instance, I would like to do the following equation for arbitrary integer $n$:
$\displaystyle R_n(t) = \int_0^t \mathrm dt' R_0(t-t') ...
7
votes
2answers
266 views
How to deduce a generator formula for a polynomial sequence?
Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule:
$$
\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
217 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 ...
6
votes
1answer
265 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
...
0
votes
0answers
154 views
Mathematica cannot compute this recursive sequence [closed]
Basically I want to compute $x_{n+1} = (1/2)(x_n + 5/x_n)$.
On Mathematica, I wrote
h[1] := 2
h[n_] := h[n + 1] = (1/2)*(h[n] + 5/h[n])
h[2]
When I tried to ...
2
votes
2answers
91 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 ...
4
votes
1answer
326 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) = ...
32
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, ...
3
votes
3answers
149 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
152 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
214 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:
...
4
votes
1answer
383 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 ...
9
votes
2answers
164 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
361 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
195 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
1k 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) & ...
