2
votes
1answer
58 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 ...
0
votes
0answers
24 views

Strassens Matrix Multiplication Algorithm to compute product of 2 4X4 Matrices

Im trying to learn starssens matrix multiplication Algorithm.So far i know that it uses 7 multiplications and replaces a multiplication by several additions and subtractions,to achieve better ...
2
votes
1answer
98 views

The Matrix Inversion Lemma: the General Case

I find it is hard to understand the application senario of the Matrix Inversion Lemma in non-special cases. Suppose I already computed $A^{-1}$ and want to find $\left(A+UCV \right)^{-1}$. The Matrix ...
0
votes
0answers
48 views

Why can I not generalize O(n^log5) for squaring matrice of size n

I have a question that is bugging me for around a 3 days, I first asked this question in stackoverflow but no one could answer it reasonably though they tried to help, so finally I found here as a ...
0
votes
0answers
154 views

Find all possible paths in a Matrix

I'm looking for algorithms to find all paths in a 4 x 4 matrix. The rules are as follows You can move in any direction (up, down, left, right, and diagonally) The next square in the path must be a ...
1
vote
1answer
115 views

How to show this algorithm on positive semidefinite matrices converges to a global maximum determinant

I'm dealing with an algorithm which is supposed to converge to the maximum determinant of certain positive semidefinite matrices. The problem is that we have such a matrix, and we vary certain ...
1
vote
0answers
21 views

Is there a method to calculate Mahalanobis distance incrementally?

By incrementally (or recursively) I mean to update the pool/group of values/vectors as soon as more vectors are available without having to recompute the entire covariance and inverse matrices. I ...
2
votes
2answers
105 views

Internet problem solving contest question

I am trying to solve a problem from the IPSC http://ipsc.ksp.sk/2001/real/problems/f.html It basically asks to compute the following recursion. ...
0
votes
0answers
90 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.
0
votes
0answers
87 views

Algorithm for reversion of power series?

Is this an algorithm for power series reversion? As input I give the alternating reciprocals of the factorial numbers: ...
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 \,,\\ ...
2
votes
1answer
97 views

Show the following matrix recursion is symmetric

I need to show the following matrix equation is symmetric and I'm not sure where to start: $A_i=\sum_{j_1=1}^{i-2}2(i-j_1-1){i-2 \choose j_1-1}A_{j_1}\Big(\sum_{j_2=1}^{i-j_1-1}{i-j_1-2 \choose ...
0
votes
1answer
124 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 ...
6
votes
1answer
413 views

Why does Strassen's algorithm work for $2\times 2$ matrices only when the number of multiplications is $7$?

I have been reading Introduction to Algorithms by Cormen et al. Before explaining Strassen algorithm the book says this: Strassen’s algorithm is not at all obvious. (This might be the biggest ...
0
votes
1answer
477 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 ...