monic
♦
7 matching pages ♦
(0.001 seconds)
7 matching pages
1: 29.21 Tables
…
►
•
Arscott and Khabaza (1962) tabulates the coefficients of the polynomials in Table 29.12.1 (normalized so that the numerically largest coefficient is unity, i.e. monic polynomials), and the corresponding eigenvalues for , . Equations from §29.6 can be used to transform to the normalization adopted in this chapter. Precision is 6S.
2: 18.4 Graphics
3: 3.5 Quadrature
…
►
Gauss–Legendre Formula
… ►Gauss–Jacobi Formula
… ►Gauss–Laguerre Formula
… ►Gauss–Hermite Formula
… ►All the monic orthogonal polynomials used with Gauss quadrature satisfy a three-term recurrence relation (§18.2(iv)): …4: 1.11 Zeros of Polynomials
…
►
§1.11(ii) Elementary Properties
… ►Every monic (coefficient of highest power is one) polynomial of odd degree with real coefficients has at least one real zero with sign opposite to that of the constant term. A monic polynomial of even degree with real coefficients has at least two zeros of opposite signs when the constant term is negative. …5: 18.2 General Orthogonal Polynomials
…
►then two special normalizations are: (i) orthonormal OP’s: , ; (ii) monic OP’s: .
…
►If the OP’s are monic, then ().
…
6: 18.38 Mathematical Applications
…
►The scaled Chebyshev polynomial , , enjoys the “minimax” property on the interval , that is, has the least maximum value among all monic polynomials of degree .
…
7: 32.8 Rational Solutions
…
►where the are monic polynomials (coefficient of highest power of is ) satisfying
…