Minimal Cubature Rules

Preface; 1. Quadrature rules and orthogonal polynomials; 2. Cubature rules: basics; 3. Orthogonal polynomials of several variables; 4. Gauss cubature rules; 5. Lower bounds for the number of nodes; 6. First minimal cubature rules; 7. Further minimal cubature rules; 8. Discrete Fourier transform and cubature rules; 9. Cubature rules and polynomial ideals; 10. Epilogue: two open problems; 11. Addendum: cubature rules on triangle and simplex; References; Index.