سوال ۲۸ کنکور ارشد علوم کامپیوتر ۱۳۹۹

Read the following passage and answer the question.

PASSAGE 3:

In our study of geometric modeling, we will make extensive use of several important mathematical techniques. The most important are linear algebra, vectors, matrix methods, determinants, set theory, polynomial interpolation, and numerical approximation. Let us briefly review some of these.

Vectors offer a distinct advantage over classic analytic geometry by minimizing our dependence on a specific coordinate system. At the very least, vectors allow us to postpone the choice of a coordinate system until the later stages of the problem-solving process. Vector operations allow us to readily determine perpendicularity or parallelism. These operations support algebraic operations while retaining geometric meaning. Section 3.1 presents a review of vectors and vector geometry.

Next we turn to matrix methods. The array of numbers that makes up a matrix can represent simply an orderly way of storing numbers pertinent to some problem or perhaps a set of polynomial equation coefficients. The rules of matrix algebra define allowable operations on these arrays. Here, the matrix performs a geometric transformation on a set of points by operating on the position vectors that define these points. This interpretation of a matrix as a geometric operator is the foundation of most geometric-modeling computations.

Now let us look at polynomial interpolation. A great deal of practical numerical analysis depends on techniques called numerical interpolation. Here, we discover the powerful but simple theorem that a straight line can be defined by, and passed through, two points, a conic curve through three points, a cubic through four, and so on. We use polynomials for interpolation, because they can be evaluated, differentiated, and integrated easily and in a finite number of steps by using just the basic arithmetic operations of addition, subtraction, and multiplication.

Question: Numerical interpolation makes use of polynomials due to -----------.