We study the roundoff error propagation in an algorithm which computes the orthonormal basis of a Krylov subspace with Householder orthonormal matrices . Moreover, we analyze special implementations of the classical GMRES algorithm, and of the Full Orthogonalization Method . These techniques approximate the solution of a large sparse linear system of equations on a sequence of Krylov subspaces ...

In this paper we present new developments of a previous work dealing with the problem of the strongly-constrained orthonormal analysis of random signals. In the former work a neural learning rule arising from the study of the dynamics of a massive system in an abstract space was introduced, and the set of equations describing the motion of such a system was directly interpreted as a learning ru...

This paper examines the use of general orthonormal bases for system identification from frequency domain data. This idea has been studied in great depth for the particular case of the orthonormal trigonometric basis. Here we show that the accuracy of the estimate can be significantly improved by rejecting the trigonometric basis in favour of a more general orthogonal basis that is able to be ad...

Given any ε > 0, we construct an orthonormal system of nk uniformly bounded polynomials of degree at most k on the unit sphere in R where nk is bigger than 1− ε times the dimension of the space of polynomials of degree at most k. Similarly we construct an orthonormal system of sections of powers A of a positive holomorphic line bundle on a compact Kähler manifold with cardinality bigger than 1−...

A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by lett...

LetM be an n-dimensional Riemannian manifold. ThenM is a differentiable manifold with a smoothly varying inner product 〈, 〉x on each tangent space TxM . An orthonormal frame at the point x ∈ M is an orthonormal basis {e1, . . . , en} of the tangent space TxM . The set of orthonormal frames at each point is isomorphic to the Lie group O(n), and the set of orthonormal frames on M forms a principa...