Levinson-type algorithms for polynomial fitting and for Cholesky and Q factors of Hankel and Vandermonde matrices

This paper presents Levinson-type algorithms for (i) polynomial fitting, (ii) obtaining a Q decomposition of Vandermonde matrices and a Cholesky factorization of Hankel matrices and (iii) obtaining the inverse of Hankel matrices. The algorithm for the least-squares solution of Hankel systems of equations, requires 3n + 9n+ 3 multiply and divide operation (MD0). The algorithm for obtaining an orthogonal representation of a (m × n) Vandermonde matrix X, and compute the Cholesky factor, F, of Hankel matrices requires 5mn+n + 2n−3m MDO. The algorithm for generating the inverse of Hankel matrices requires 3(n +n−2)/2 MDO. Our algorithms have been tested by fitting polynomials of various orders and Fortran versions of all subroutines are provided in appendix.