Orthonormal polynomials in one and two dimensions: application to calibration problems in high energy physics

摘要

Calibration problems in high energy physics lead to ill-posed inverse problems. The numerical generation of special polynomials which are orthonormal over discrete point sets is described. Such polynomials, when used as a functional basis, allow to reach an optimum (unit) condition number. Results from computer codes which generate orthonormal polynomials in one and two independent variables are reported and their applications to specific calibration problems are discussed.