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searching for Three-term recurrence relation 12 found (17 total)

alternate case: three-term recurrence relation

Clenshaw algorithm (2,163 words) [view diff] exact match in snippet view article find links to article

applies to any class of functions that can be defined by a three-term recurrence relation. In full generality, the Clenshaw algorithm computes the weighted

Generalized minimal residual method (3,328 words) [view diff] exact match in snippet view article find links to article

Unlike the unsymmetric case, the MinRes method is given by a three-term recurrence relation. It can be shown that there is no Krylov subspace method for

Kravchuk polynomials (896 words) [view diff] exact match in snippet view article find links to article

q){z^{k}}.\end{aligned}}} The Kravchuk polynomials satisfy the three-term recurrence relation x K k ( x ; n , q ) = − q ( n − k ) K k + 1 ( x ; n , q ) +

Tridiagonal matrix (2,707 words) [view diff] exact match in snippet view article find links to article

of a tridiagonal matrix A of order n can be computed from a three-term recurrence relation. Write f1 = |a1| = a1 (i.e., f1 is the determinant of the 1

Gaussian quadrature (6,792 words) [view diff] exact match in snippet view article find links to article

Gaussian quadrature), the recurrence relation reduces to a three-term recurrence relation: For s < r − 1 , x p s {\displaystyle s<r-1,xp_{s}} is a polynomial

Christoffel–Darboux formula (2,055 words) [view diff] case mismatch in snippet view article find links to article

(2021-08-01). "Asymptotic Behaviour of Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I". Constructive Approximation. 54 (1): 49–116. arXiv:1909.09107

Gauss–Legendre quadrature (1,616 words) [view diff] no match in snippet view article find links to article

their method for computing Gaussian quadrature rules given the three term recurrence relation that the underlying orthogonal polynomials satisfy. They reduce

Legendre polynomials (6,711 words) [view diff] exact match in snippet view article find links to article

kind. As discussed above, the Legendre polynomials obey the three-term recurrence relation known as Bonnet's recursion formula given by ( n + 1 ) P n +

Zernike polynomials (6,471 words) [view diff] exact match in snippet view article find links to article

R_{m+2}^{m}(\rho )=((m+2)\rho ^{2}-(m+1))\rho ^{m}} . The following three-term recurrence relation then allows to calculate all other R n m ( ρ ) {\displaystyle

Lanczos algorithm (8,287 words) [view diff] exact match in snippet view article find links to article

why sequences of orthogonal polynomials can always be given a three-term recurrence relation.) For k = j − 1 {\displaystyle k=j-1} one gets h j − 1 , j =

Mathieu function (8,390 words) [view diff] exact match in snippet view article find links to article

implementing a backwards recurrence algorithm. The complexity of the three-term recurrence relation is one of the reasons there are few simple formulas and identities

Marcum Q-function (7,425 words) [view diff] exact match in snippet view article find links to article

representation of the generalized Marcum Q-function. The related three-term recurrence relation is given by Q ν + 1 ( a , b ) − ( 1 + c ν ( a , b ) ) Q ν (