Questions tagged [recursion]
For questions about defining recursive functions, recursive algorithms and solving recursive equations.
659
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How to Set Precision for an RSOLVE Problem
The following code was working fine -- now it produces errors. I originally built this in ver 13.1 and I'm now running ver 14. I think I'm getting machine precision errors after k=11 that were not ...
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How to fix parameter locally for iterating recursion equations
The following is a simplified version of a more detailed problem.
I have two coupled recursion equations of two variables, x and y. One equation also depends on a parameter, c:
...
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Return[] in Recursive Functions [duplicate]
Here is the pseudocode I am using to demonstrate the problem.
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RecurrenceTable vs For loop : they do not give the same results. Why?
I have a second-order recurrence equation that I want to plot.
I've used two different methods.
The first uses RecurrenceTable, the second uses a traditional ...
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Most efficient way of defining the following sets for every step $n$
For each $n\in\mathbb{N}$, how do we compute sets $A_n$ and $B_n$ below:
Let $A_1=[0,2/3)$. Let $B_1=(2/3,1]$.
If $A_n$ is a union of intervals, then for each interval cut out the
middle $1/2^{n+1}$ ...
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RSolve does not evaluate this recursion with two boundary conditions
I am using RSolve to solve for a function defined recursively, with two boundary conditions:
First boundary condition describes the relationship between $f(1)$ and $f(0)$
Second boundary condition ...
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86
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Strange errors of exceeding RecursionLimit in a function with two arguments, one set delayed and one fixed
INTRODUCTION
Hi. I feel a bit embarrased asking this question as the answer may be staring me in the face and there are at least two other stackexchange articles related to it.
MINIMAL WORKING EXAMPLE
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Recursion limit for NDSolve
I have a fairly complex equation containing many terms, I can use the NDSolve for solving the differential equation for lesser terms (6400ish). But can't do it for ...
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Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?
I have an ordinary differential equation and want to solve it using power series as ψ[x_] = Sum[Subscript[a, n] x^n, {n, 0, ∞}] to obtain the recurrence relation ...
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1
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Root finding for holomorphic functions, II
This is a follow-up to my question Root finding for holomorphic functions. I am trying to compute $10^6$ zeros of the derivative of the Riemann zeta function $\zeta(s)$ in the critical strip near ...
- 1,161
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Solving a System of Recursively Defined Equations in Mathematica
I am trying to solve a system of equations in Mathematica where the variables are recursively defined. The system represents a probability distribution, and I want to find the values of the variables ...
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Finding the limit of a recursive sequence
I have come across a few different questions relating to my issue (namely this one, but the answers are not working for me. Here are my inputs;
...
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How is my code going over the recursion limit?
I don't know how my code is exceeding the recursion limit of 1024.
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1
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Recursion not working for higher terms
I am trying to find the terms x9,x10,x11 and y6,y7,y8 and so on from the recursive relation given in the code.
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Sorting a list of functions by exploiting the recursive structure
Given a list of functions list and a vector of arguments {t, a}:
...
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Calculate Bernoulli numbers ( with a twist) [closed]
Mathematica has an inbuilt function BernoulliB that calculates $B_n$ for which,
$$\frac{t} {\left(e^t-1\right)}=\sum_{n=0}^{\infty} \frac{B_n}{n !}t^n $$
I need to ...
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Understanding HoldFirst in QuickSort algorithm
I have read the implementation of QuickSort algorithm in WL from Roman Maeder's Computer Science with Mathematica (2000).
The implementation is shown below.
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Recurrence formula evaluating with speacial counting of subscripts
Hoping to check some recurrance relationship like this
$a_1 = x$ and $a_2 = y$, with
$$
a_{2n+1} = a_{2n} a_{2n-1}
$$
and
$$
a_{2n+2} = a_{2n+1} + 4
$$
Tried
...
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2
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107
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Optimization of a Markov сhain with symbolic transition rate
I am trying to work on 1D random walk that can move to left, right or stay with probabilities $p_i$,$q_i$,$r_i$ that changes with the site $i$. I am trying to simulate this by using a recurrence ...
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How do you Solve a Simultaneous System of Recursions
Consider the following system of simultaneous recursions:
r[n] == s[n-1]
s[n-2] == r[n-3]
I am tring to solve this system (I have given a vastly simplified ...
1
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2
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92
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Recursively applying a substitution
I have an expression like this:
2v[j-1]-(s[j]+1)(c[j]-c[j-1]) >= v[j]
I want to apply this recursively say k times. I can do one step like this:
...
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Implementing recurrence relation for an integral
I would like to implement the following recurrence relation,
$$I_{n+1}=-\log(2)I_n-\sum_{k=1}^n(-1)^k\left(1-\frac{1}{2^k}\right)\frac{n!\zeta(k+1)}{(n-k)!}I_{n-k}$$
with initial conditions,
$$I_0=\...
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How to write a recursive formula?
What is the Mathematica command for the recursive formula:
F[a_]:=Sum[(-1)^a Binomial[a,k] Log[2]^(a-k) F[k], {k,0,a}]
where
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RSolve for system of equations and matrix power [closed]
I have a matrix
a = {{3, -2}, {2, -2}};
We can easily find the n-th power, $A^n$ using
MatrixPower[a,n]
We can also find the ...
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How can I compute the $n$-th complete Bell polynomial?
I'm interested in computing the n-th complete Bell polynomial
$
B_n(x_1,..., x_n)
$ using the formula given as the last equation in the "Exponential Bell polynomials" section here (I tried ...
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How to obtain terms defined by a recursion relation in terms of the first value without solving the recursion?
I have a set of coefficients $A_{i}^N$ where $i=0,\dots, N$ that obey a recursion relation that takes the form
$$A_i^N = C_i^N-\sum_{M=1}^N\sum_{k=0}^{N-M}A_k^{N-M}\psi_{i,k}^{N,M}$$
The coefficients $...
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How is this type of piecewise function represented and calculated? [closed]
How is this type of piecewise function as follows in the picture represented and calculated?
Use:
...
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