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

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3
votes
4answers
320 views

Recursive function for calculating the arithmetic mean of a vector

I want to write recursive function for calculating the arithmetic mean of a vector. For $X(n)=\{1,2,3,\ldots, n\}$, the formula is ${\rm Mean}(X(n))=((n-1)\, {\rm Mean}((X(n-1))+X_n)/n$. My ...
4
votes
3answers
156 views

Long waiting time for computing a summation

It takes a long time to compute the summation below, and I'd like to know if there are alternative ways to compute things faster. When replacing $15$ by $\infty$, then I should get $3^{1/3}$. I need ...
2
votes
2answers
267 views

Recursive formula involving a piecewise function

I am trying to construct a recursion, g[t], where g[t] = a[t] if g[t-1] = 1 ...
6
votes
1answer
224 views

How can I define a Listable function only apply to a vector?

Consider the function f which should behave as f[{{1, 2}, {3, 4}, {5, 6, 7}}] ...
8
votes
3answers
404 views

Create sine function with random increase in phase

I am trying to simulate a signal that randomly increases its phase, so far I have tried two thing but neither worked. I usually use matlab but I want to learn some Mathematica so I thought I would try ...
0
votes
1answer
127 views

fit recursive function to data

I have a function $g(x, n)$, which is a recursive expression: $x$ is a variable and $n$ the number of iterations. In my case $n=3$ for all $x$. An example is the following: ...
2
votes
1answer
138 views

Integral of GeneratingFunction

I know that GeneratingFunction can be used to compute the generating function $\sum_{n=0}^\infty a_n x^n$ of a sequence $(a_n)_n$ via GeneratingFunction[a[n],n,x] ...
7
votes
0answers
241 views

Compile recursive function modifying global variables

How to compile recursive formula when it relies on more than a few global variables (global to the topmost compiled function)? It is unreasonable to pass on all such variables to each recursive ...
3
votes
1answer
255 views

Transform recursion for coefficients into differential equation for generating function

Assume, one is given a linear recursion with polynomial coefficients for a sequence $(a_i)_i$, such as a[i] == i a[i-1] I would like to convert this recursion ...
7
votes
2answers
316 views

How can I define a sequence of functions?

I need to define a function fun, and then re-define this function iteratively. The code is given at the end. First, a function ...
1
vote
1answer
226 views

How can I solve my recursion equation?

How can I solve the recursion equation given below? I doubt there have no solution for the recursion equation because this is circulating recucrsion equation. ...
3
votes
1answer
159 views

Converting this recursive function definition into nested sums?

Here's the recursive function I'm using: DH[n_, k_, s_] := Sum[Binomial[k, k - j] DH[n/m^j, k - j, m + 1], {m, s, n^(1/k)}, {j, 1, k}] DH[n_, 0, s_] := 1 Now, ...
6
votes
1answer
141 views

Recurrences of lists

Assume we have a multi-dimensional recurrence, e.g. $\qquad\begin{align*} a_1 &= (1,2) \\ a_n &= (1,2) + a_{n-1} \quad, n>1 \end{align*}$ with the easy solution $a_n = (n,2n)$. How ...
3
votes
2answers
167 views

Implementation of a recurrence relation for the polynomials appearing in the large order asymptotics of the Bessel functions

I would like to implement the recurrence relation for the polynomials $U_n(x)$ appearing in the large order asymptotics of the Bessel functions. The recurrence in question is ...
1
vote
4answers
330 views

Recurrence relation in a table

I am trying to generate a list of x-values for a function using a module, where my x-value must increase by 'a' if the term ...
4
votes
0answers
113 views

Efficient Generation of Subgraphs (or, unfriend a friend a day)

NB: If you're not interested in the back-story, you could simply jump forward to the code which I'm seeking to optimize. Also, I believe this code would only work for MMA 8.0 and above. My friends ...
0
votes
0answers
30 views

Keeping memory to reduce the running time of recursion [duplicate]

I am using the following recursion in Mathematica to compute W[n, 1, s] for given n and s: ...
8
votes
5answers
271 views

Wrapping a function in count

I am working through the Programming Paradigms via Mathematica (A First Course) and am attempting to answer the following: Use recursion to count how many times the argument can have its square ...
8
votes
4answers
378 views

Partitioning a list by recursion (Programming Paradigms via Mathematica (A First Course))

I am working through the course Programming Paradigms via Mathematica. One of the homework exercises for the section Recursion I: Passing the Buck is as follows: Use recursion to partition a ...
1
vote
2answers
96 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
135 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
376 views

Recursion depth exceeded

Below is my code for numerical solving of PDE with Crank Nicolson scheme. ...
4
votes
3answers
150 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
252 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
109 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
248 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
487 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
90 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
99 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
284 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 ...
2
votes
0answers
187 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?
5
votes
0answers
196 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
149 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
103 views

Recursion and safety of SetAttributes[Function, SequenceHold]

Compare the timings below ...
5
votes
2answers
208 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
915 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
750 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
129 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
95 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
122 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
156 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
601 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
184 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. ...
3
votes
1answer
161 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
175 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
180 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
234 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
571 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
129 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
272 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 ...