Concepts inPolynomial approximation in handwriting recognition
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by best and simpler will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials.
more from Wikipedia
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x ¿ x/4 + 7 is a polynomial, but x ¿ 4/x + 7x is not, because its second term involves division by the variable x (4/x), and also because its third term contains an exponent that is not an integer (3/2).
more from Wikipedia
Handwriting recognition
Handwriting recognition is the ability of a computer to receive and interpret intelligible handwritten input from sources such as paper documents, photographs, touch-screens and other devices. The image of the written text may be sensed "off line" from a piece of paper by optical scanning or intelligent word recognition. Alternatively, the movements of the pen tip may be sensed "on line", for example by a pen-based computer screen surface.
more from Wikipedia
Plane curve
In mathematics, a plane curve is a curve in a Euclidean plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. A smooth plane curve is a curve in a real Euclidean plane R and is a one-dimensional smooth manifold. Equivalently, a smooth plane curve can be given locally by an equation {{{1}}} where ¿ : R ¿ R is a smooth function, and the partial derivatives ¿¿/¿x and ¿¿/¿y are never both 0.
more from Wikipedia
Parametric equation
the butterfly curve. ]] In mathematics, parametric equation is a method of defining a relation using parameters. A simple kinematic example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion. Abstractly, a parametric equation defines a relation as a set of equations. Therefore, it is somewhat more accurately defined as a parametric representation. It is part of regular parametric representation.
more from Wikipedia
Orthogonality
Orthogonality comes from the Greek orthos, meaning "straight", and gonia, meaning "angle". It has somewhat different meanings depending on the context, but most involve the idea of perpendicular, non-overlapping, varying independently, or uncorrelated. In mathematics, two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors are orthogonal if and only if their dot product is zero.
more from Wikipedia
Vector space
A vector space is a mathematical structure formed by a collection of elements called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.
more from Wikipedia
Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the expression. For instance in the first three terms respectively have the coefficients 7, ¿3, and 1.5 (in the third term the variables are hidden, so the coefficient is the term itself; it is called the constant term or constant coefficient of this expression).
more from Wikipedia