Algorithm 1 again fails because it attempts to

diagonalize A, obtaining a matrix V with condition number K(V) = 2.

In other words, the transform that

diagonalizes the matrix A is known only in special cases, such as in the case of strongly symmetric PSFs and reflective and anti-reflective BCs (see [9, 12] and references therein).

Our Matlab RULE routine simply uses EIG to

diagonalize the matrix [T.

Therefore to complete our task we need to

diagonalize the operator H, i.

We

diagonalize this self-adjoint bounded operator and find its spectrum with the aid of the second operator I, which corresponds to a q-difference equation for the same set of polynomials.

Compute the matrix V of eigenvectors which

diagonalizes the covariance matrix C:

it

diagonalizes [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In a basis which

diagonalizes [[left and right arrow][epsilon]] ([[vector].

An angular basis set is used which

diagonalizes the rotational (J > 0) part of the total kinetic energy.

j] a matrix that

diagonalizes simultaneously the matrices [?

A primitive angular basis set is constructed which

diagonalizes the rotational (J > 0) kinetic energy operator; subsequently, this basis is contracted through a series of diagonalizations of smaller Hamiltonian matrices.

And (to a fair approximation) a preferred basis will arise naturally, within the quasi-classical domain, as the basis which, under coarse-graining,

diagonalizes the decohering variables.