Calculation of zeros of orthogonal polynomials. (Russian. English summary) Zbl 1012.65507
Summary: We present an algorithm that makes it possible to find the zeros of classical higher-order orthogonal polynomials. The method is based on the relationship between the zeros of these polynomials and the eigenvalues of tridiagonal symmetric matrices of a special form. To increase the accuracy of calculation we use an additional iteration. We give computational formulas for Jacobi, Lagrange and Hermite polynomials.
MSC:
| 65H05 | Numerical computation of solutions to single equations |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 26C10 | Real polynomials: location of zeros |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 65D20 | Computation of special functions and constants, construction of tables |
