سوال ۲۷ کنکور ارشد علوم کامپیوتر ۱۴۰۰

Read the following passage and answer the question.

PASSAGE 3: Structure, Sparsity, and Black Boxes

Large matrices, perhaps in excess of $10^{5}$, arise routinely in scientific problems — for example, as representations of three forces in a structure, or, between thirty species in large matrices. By contrast, usually arise indirectly in the discretization of partial differential or integral equations. One might say that if $m$ is very large, the approximation to $\infty$. It follows that most large matrices of computational interest are simpler than their vast numbers of individual entries might suggest, exhibiting some kind of structure.

The most obvious structure that a large matrix may have is a preponderance of zero entries. (The opposite of sparse is dense.) A matrix arising from the finite-difference discretization of a partial differential equation may have dimension $m = 10^{5}$ with only $\approx 10$ nonzero entries per row. This kind of sparsity is readily exploited by the iterative methods we shall discuss, for they only need to manipulate the matrix in the form of a black box:

$x \longrightarrow \boxed{\text{BLACK BOX}} \longrightarrow Ax.$

The iterative algorithm requires nothing more than the ability to determine $Ax$ for any $x$, which in a computer program will be effected by a procedure whose internal workings need be of no concern to the designer of the iterative algorithm. Such a procedure may require the computation of $A \cdot x$. For the example of a sparse matrix $A$, such a procedure to compute $Ax$ is only $O(vm)$ rather than $O(m^{2})$ operations. This is in contrast to the algorithms of direct linear algebra, such as Gaussian elimination or triangularization, which explicitly manipulate matrix entries and in the process generally destroy sparsity.

Question: According to the passage, a structure in a matrix ----------.