Figure 7 Spatial linear interpolation at interpolated frame.
At each interpolation step the parameters are reoptimized in order to describe the newly interpolated data.
A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points.
Guarantees of closed-loop quadratic stability and performance at intermediate interpolation points are presented in terms of a set of linear matrix inequalities (LMIs).
The polynomial or trigonometric interpolant of an arbitrary function f(x) may be represented as a "cardinal function" series whose coefficients are the values of f(x) at the interpolation points.
Guruswami and Sudan (GS) presented an improvement on Sudan's algorithm [11], by introducing a multiplicity at each interpolation point.
Then, we compute the coordinates of the pixel in the reference element (see Fig. 1) and the corresponding basis functions at the interpolation nodes.
The curve does not have to be smooth at the interpolation nodes: for example, curve representing symbols, signature, handwriting or other specific data.
The function for PNC calculations is chosen individually at each interpolation and represents the probability distribution function of parameter (alpha in ) [0; 1] for every point situated between two interpolation knots.
Remark 2.5 Upon substituting k = a = b = 1 and β = ξ u into (13), we arrive at the interpolation function for twisted generalized Eulerian numbers and polynomials, which is given as follows: l 1 ( u ξ, s, χ ) = L χ, ξ u ( s, x ; 1, 1, 1 ), where, for a positive integer r, ξ is the r th root of 1. l 1 ( u ξ, s ; χ ) = ∑ m = 0 ∞ ( ξ u ) m χ ( m ) ( m + x ) s. (cf. [18]).
