CG, SYMMLQ, and MINRES are Krylóv subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ’s solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This underst...

The Arnoldi method is currently a very popular algorithm to solve large-scale eigenvalue problems. The main goal of this paper is to generalize the Arnoldi method to the characteristic equation of a delay-differential equation (DDE), here called a delay eigenvalue problem (DEP). The DDE can equivalently be expressed with a linear infinite dimensional operator whose eigenvalues are the solutions...

Abstract. Let φm be a polynomial satisfying some mild conditions. Given a set R ⊂ C, a continuous function f on R and its best approximation p n−1 from Πn−1 with respect to the maximum norm, we show that p ∗ n−1 ◦φm is a best approximation to f ◦ φm on the inverse polynomial image S of R, i.e. φm(S) = R, where the extremal signature is given explicitly. A similar result is presented for constra...

We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449–1466]. For a given semi-rational polytope p and a rational subspace L, we integrate a given polynomial function h over all lattice slices of the polytope p parallel to the subspace L and sum...

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A cent...

A twisted sum Z of two Banach spaces X and Y is defined (see [11]) through a short exact sequence: 0 −→ X −→ Z −→ Y −→ 0. These short exact sequences in the category of (quasi-)Banach spaces are considered naturally in the investigation of three space properties (a property P in the category of quasi-Banach spaces is called a three space property if for every short exact sequence as above, Z ha...

This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundation for this study. For any vector space W , we study what we call quasi compatible subsets of Hom(W,W ((x))) and we prove that any maximal quasi compatible subspace has a natural nonlocal (namely noncom...

A modified four-dimensional linear active disturbance rejection control (LADRC) strategy is proposed for a dual three-phase permanent magnet synchronous generator (DTP-PMSG) system to reduce cross-coupling between the d and q axis currents in d-q subspace harmonic x-y subspace. In subspace, uses model-based LADRC enhance decoupling effect axes ability against parameter variation. 5th 7th curren...

We present two characterizations of Lagrange interpolation sets for weak Chebyshev spaces. The rst of them is valid for an arbitrary weak Chebyshev space U and is based on an analysis of the structure of zero sets of functions in U extending Stockenberg's theorem. The second one holds for all weak Chebyshev spaces that possess a locally linearly independent basis. x1. Introduction Let U denote ...