Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving Linear System of Equations Via A Convex Hull Algorithm   We present new iterative algorithms for solving a square linear system $Ax=b$
in dimension $n$ by employing the {\it Triangle Algorithm} \cite{kal12}, a
fully polynomial-time approximation scheme for testing if the convex hull of a
finite set of points in a Euclidean space contains a given point. By converting
$Ax=b$ into a convex hull problem and solving via the Triangle Algorithm,
together with a {\it sensitivity theorem}, we compute in $O(n^2\epsilon^{-2})$
arithmetic operations an approximate solution satisfying $\Vert Ax_\epsilon - b
\Vert \leq \epsilon \rho$, where $\rho= \max \{\Vert a_1 \Vert,..., \Vert a_n
\Vert, \Vert b \Vert \}$, and $a_i$ is the $i$-th column of $A$. In another
approach we apply the Triangle Algorithm incrementally, solving a sequence of
convex hull problems while repeatedly employing a {\it distance duality}. The
simplicity and theoretical complexity bounds of the proposed algorithms,
requiring no structural restrictions on the matrix $A$, suggest their potential
practicality, offering alternatives to the existing exact and iterative
methods, especially for large scale linear systems. The assessment of
computational performance however is the subject of future experimentations.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom