Multinomial Lagrange-Bernstein approximants

The well-known Bernstein polynomials are frequently used in signal representation, finite impulse response filter realization, computer-aided geometric design, and B-spline techniques. In this letter, a refinement of the Bernstein approximation scheme for complex exponentials, by making use of a judicious Lagrange interpolation scheme, is proposed. Applied to a general function, this approach leads to a new polynomial approximant, termed a multinomial Lagrange-Bernstein approximant, that performs better than the usual Bernstein approximant.