Search results
Results from the WOW.Com Content Network
Given a quadratic polynomial of the form + the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point) of the parabola. That is, h is the x -coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h ), and k is the minimum value (or maximum value, if a < 0) of the quadratic ...
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]
It can be shown that the degree of a polynomial over a field satisfies all of the requirements of the norm function in the euclidean domain. That is, given two polynomials f(x) and g(x), the degree of the product f(x)g(x) must be larger than both the degrees of f and g individually. In fact, something stronger holds:
Any nth degree polynomial has exactly n roots in the complex plane, if counted according to multiplicity. So if f(x) is a polynomial with real coefficients which does not have a root at 0 (that is a polynomial with a nonzero constant term) then the minimum number of nonreal roots is equal to (+),
Horner's method evaluates a polynomial using repeated bracketing: + + + + + = + (+ (+ (+ + (+)))). This method reduces the number of multiplications and additions to just Horner's method is so common that a computer instruction "multiply–accumulate operation" has been added to many computer processors, which allow doing the addition and multiplication operations in one combined step.
Polynomials of small degree have been given specific names. A polynomial of degree zero is a constant polynomial, or simply a constant. Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. [8]
where n is a non-negative integer that defines the degree of the polynomial. A polynomial with a degree of 0 is simply a constant function; with a degree of 1 is a line; with a degree of 2 is a quadratic; with a degree of 3 is a cubic, and so on. Historically, polynomial models are among the most frequently used empirical models for curve fitting.
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...