For questions about defining recursive functions, recursive algorithms and solving recursive equations (e.g, with `RSolve`)
2
votes
2answers
53 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, ...
1
vote
0answers
74 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 ...
1
vote
0answers
63 views
Nonlinear recurrence relation
I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{nā1})^3)} 3$$
Is there another way to get a formula for the nth term?
4
votes
0answers
84 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
62 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
...
4
votes
2answers
107 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 ...
20
votes
4answers
511 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
199 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
78 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
66 views
Notation not recursive enough?
My notation is not recursing enough. For example,
Notation[W[a_ | b_] ā¹ foo[a_, b_]/foo[b_]]
Notation[W[a__, b_ | c_] ā¹ 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
101 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
274 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
102 views
Am I entering this 2-variable recurrence correctly?
I'm trying to solve this recurrence with two variables.
...
2
votes
1answer
102 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 ...
