부산대학교 도서관

In this paper, we consider bi-variate Logarithmic functions over two dimensional box. We convert the bi-variate differentiable logarithmic functions to Lagrange's polynomials of two variables and finite degree. Subsequently, we expand the Lagrange polynomial onto Bernstein form over the same domain. Furthermore, we prove that the Lagrange polynomial is optimized by the Bernstein enclosure with error bound. If the error is not bounded, we optimize the alternative discrete Logarithmic functions by the enclosure bound at the corresponding values of the given nodes. Eventually, we extend Bernstein properties to the Bernstein-Lagrange Form.