2
votes
1answer
57 views

Recurrence - using power series

Could you help me in solving this recursion( a closed form ) using power series $\mu(n)=\mu(n−1)k_0+(n−1)\mu(n−2) k_1 \tag 1$, where $k_0,k_1$ are constants $\mu(0)=3,\mu(1)=5$ HINT: We can think ...
1
vote
1answer
48 views

Infinite series for recurrence

Question 1 If I define $A(z) = \sum_{n \ge 0} a_n \frac{z^n}{n!} \tag 1$ (where $a_n$ are $3\times 3$ constant matrices indexed with n), then can we re-write $\sum_{n \ge 1} a_{n-1} \frac{z^n}{n!} ...
0
votes
0answers
23 views

Solving a simple Recurrence in summation form(very special case)

I have a bit confusing recursion form $\sum_{n=2}^{\infty}\{f(n)\frac{n}{n-1}\}=C, \tag 1$ $f(0)=b,f(1)= a,f(2)=c$ and $C$ are constants. Could you help me to solve this recursion or help me to ...
1
vote
0answers
50 views

Solving the recursion $F(n)=K_0F(n-1)/(n-1)+K_1F(n-2)/(n-2)$

Please help me in solving the recursion $F(n)=K_0\frac{F(n-1)}{n-1}+K_1\frac{F(n-2)}{n-2}$, preferably using power series for the values of $F(n)$ in terms of $n$. Here $K_1$ and $K_2$ are ...
5
votes
3answers
361 views

Recurrence with varying coefficient

Problem 1 $$ {\rm f}\left(n\right) = \frac{1}{n}\, \left[{\rm f}\left(n - 1\right)k_{0} + {\rm f}\left(n-2\right)k_{1}\right]\tag{1} $$ ( This can also be written as ${\rm Q}\left(n\right) = ...
7
votes
3answers
219 views

Solving recurrence relation: Product form

Please help in finding the solution of this recursion. $$f(n)=\frac{f(n-1) \cdot f(n-2)}{n},$$ where $ f(1)=1$ and $f(2)=2$.
0
votes
0answers
81 views

Strassen's Matrix Multiplication Example Problem

How to multiply two matrices using strassen's matrix multiplication.I have only learned the theory part but i cannot find any examples on the net. Could some one explain with two 2X2 Matrices.
1
vote
0answers
131 views

How to compute this recursion in linear time?

Can the following iterative update on a $n$-element vector $\mathbf{x}_t$ be computed in $O(n)$ computations? \begin{align*} \mathbf{x}_{t+1} & = a_t\mathbf{y}_t + \mathbf{A}_t \mathbf{x}_t \,,\\ ...
0
votes
1answer
121 views

Solving recursive relations using matrix method.

I am looking to solve the recursive relation $P_n=2P_{(n-2)}+3P_{(n-3)}+7P_{(n-7)}$ using the matrix method. The matrix method solves the recursive relation in ...
5
votes
2answers
212 views

Repertoire method for solving recursions

I am trying to solve this four parameter recurrence from exercise 1.16 in Concrete Mathematics: $g(1) = \alpha;$ $g(2n+j) = 3g(n) + γn + β_j$ : j = 0,1 and n >= 1 I have assumed the closed form to ...
13
votes
6answers
1k views

How to solve this recurrence relation? $f_n = 3f_{n-1} + 12(-1)^n$

How to solve this particular recurrence relation ? $$f_n = 3f_{n-1} + 12(-1)^n,\quad f_1 = 0$$ such that $f_2 = 12, f_3 = 24$ and so on. I tried out a lot but due to $(-1)^n$ I am not able to ...
2
votes
1answer
219 views

Is there a formula for nCr that considers a min/max range? (restricted composition estimation)

I'm bad at math and hope I explain this right(please don't be upset if I don't, I'm not trying to be lazy or a jerk, I really don't understand what information is sometimes required and focus on the ...
0
votes
1answer
473 views

calculating matrix rank with gaussian elimination

[The answer to my problem has been found: it was a simple sign error. the pseudo code below is fine] I have implemented an algorithm in c++ that should calculate the matrix rank of a given n x m ...