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# Questions tagged [linear-algebra]

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10 views

### Best algorithm for computing the log-determinant

I am diving into some literature to understand which is the best algorithm for computing the log-determinant of a PSD matrix. So far I have found the following two papers: Large-scale Log-...
17 views

### Are there practical usage of determinants in numerical simulation?

I know the historical importance of the link between linear systems and determinants. I also know that determinants have a beautiful connection with non-singular matrices, i.e., if a matrix is non-...
36 views

### What is the complexity of finding e^(A) for a Hermitian matrix A?

If A is a hermitian matrix of size NxN .What is the order of no. of steps required to compute e^(A).How to prove it?
7 views

### Looking for good book similar Stability/Conditioning in Numerical Linear Algebra,

I am currently reading Numerical Linear Algebra by Trefethen and Bau and I am finding it quite difficult to read. In particular, I have been trying to read the sections on Floating Point Arithmetic, ...
30 views

### Check the Complexity time of Power method

Hi i have write a function in Matlab to calculate the power method and i wont to find the time complexity. ...
20 views

### Minimal subset of rows that generate smaller polyhedron

Given a matrix $[A|B]$ I want to find a minimal matrix $[A'|B'] \subseteq [A|B]$ (i.e. the rows in $[A'|B']$ are also in $[A|B]$) such that $A'x < B' \Rightarrow Ax < B$. Geometrically, I want ...
33 views

### Given a system in $\mathbb{F}_2$ in RREF, how do I find a solution of minimal norm?

I have a $12 \times 12$ (so not really large) system of linear equations in $\mathbb{F}_2$ which I got to RREF through the usual row reduction. Suppose the system has multiple solutions, and call the ...
25 views

### How do you solve a general linear diophantine equation in polynomial time (with minimization constraint)?

Given $$a_1 X_1 + \dots + a_n X_n = b$$ where $a_i, b \in \Bbb{Z}$. How do you come up with a clearer picture of the solution set in polynomial time. Also, what I really want is to do the above,...
14 views

### Convergence of Conjugate gradient method

I have implemented my own matrix library in Java to solve fluid simulations. So I have also implemented the conjugate gradient method and I got a little bit confused. What I have done to test my CG-...
29 views

### Recover boolean vector from dot products

Question: I want to determine a boolean vector $b \in \{0,1\}^n$ consisting of zeros and ones, but cannot access it directly. I can only call a black-box computer code which will take the dot product ...
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398 views

### Applications of the LU factorization in computer science [closed]

I have been searching for the applications of the LU factorization/decomposition in computer science. From Wikipedia, I have found some of the applications, but these don't seem to be relevant to ...