Bernstein polynomial
Polinomio de Bernstein
- Date
- 1912 · confidence high
- Place
- Kharkiv, Ukraine
- Credited to
- Sergei Bernstein
- Field
- Knowledge & symbols
What was discovered
A polynomial expressed as a linear combination of a special basis (the Bernstein basis polynomials), used by its author to give a constructive proof of the Weierstrass approximation theorem. With the advent of computers it became central to Bézier curves in computer-aided design.
Bernstein introduced them in 1912; their practical importance grew decades later with computer graphics and Bézier curves.
What it led to
- a constructive proof of the Weierstrass approximation theorem
- the mathematical basis of Bézier curves and surfaces
- the De Casteljau algorithm for stable evaluation