Showing papers on "Biorthogonal system published in 1983"

On the practical use of the lanczos algorithm in finite element applications to vibration and bifurcation problems

Abstract: Vibration and bifurcation analyses of structures modeled by finite elements yield a linear eigenvalue problem, Kq = λ Bq, where K and B are symmetric matrices of large dimension in practical applications. An interative reduction of the matrix size is attained by the biorthogonal Lanczos algorithm which allows extraction of the lower eigenvalue spectrum. For solving the problem when coincident eigenvalues occur, a restart procedure is implemented so that further iterations can be performed from a new arbitrary vector, yielding thus to modifications in the interaction eigenvalue problem.

$q$-analogs of some biorthogonal functions

Abstract: Abstract In this note we obtain a q-analog of a pair of biorthogonal sets of rational functions which have been obtained recently by M. Rahman in connection with the addition theorem for the Hahn polynomials.

Fundamental biorthogonal systems and projection bases in banach spaces

Abstract: Let X be a Banach space and X* its dual space. A system x~, f~, x~ X,f~ X*, i~] (I being some set) is said to be biorthogonal if /~(xj)= ~j (8 is Kronecker's delta). A biorthogonal system is fundamental if the closed linear hull [x d i ~f]----76; if, furthermore, the set (fi) is total on X, then the system x i, fi is called an M-basis. An M-basis which can be well-ordered in such a way that for all ~ there exist collectively bounded projectors P~: X--~ [x~\" ~ <~] parallel to [x~: ~ ~ ~] is called a projection basis. If the norms of all projectors are equal to i, a basis is said to be monotonic. It is readily seen that the definition of a projection basis stated above is equivalent to the definition in [i, 2]. We say that a biorthogonal system xi, fi, i~f , isbounded by a number a if sup~ex~xi~fl~.~

On the magnetic interactions between ions with degenerate π-orbitals

Abstract: An effective Hamiltonian is presented which describes the interaction between two orbitally degenerate magnetic ions in D∞h symmetry The parameters appearing in the Hamiltonian are related to explicit expressions arising from a perturbation formalism previously described Using either Lowdin-orthogonalized or biorthogonal basis sets, constructed from overlapping atomic orbitals, quantitative values for the parameters can be obtained Numerical applications are given for B2 and O2, treating these molecules as simple π-π and π3-π systems, respectively Both types of basis sets yield similar qualitative features of the level schemes and explain also the order of ground and low-lying excited states in the O2-molecule Comparing the results from the perturbation calculations with those obtained from a complete configuration interaction treatment, and also from experiments, it is found that the biorthogonal sets lead, at least for the systems considered, to a better agreement Empirical corrections improving the small-basis-set approach are examined

On an Inequality of Devore

Abstract: The aim of this note is to present an elementary functional-analytical proof of a Bernstein-type inequality, given by DeVore in 1973 for one-dimensional trigonometric polynomials. This proof allows extensions of the inequality to arbitrary total biorthogonal systems in Banach spaces. Furthermore, the general inequality may indeed be used to prove a uniform-boundedness principle with rates.