On a 2-Orthogonal Polynomial Sequence via Quadratic Decomposition

On orthogonal polynomials obtained via polynomial mappings

Let (pn)n be a given monic orthogonal polynomial sequence (OPS) and k a fixed positive integer number such that k ≥ 2. We discuss conditions under which this OPS originates from a polynomial mapping in the following sense: to find another monic OPS (qn)n and two polynomials πk and θm , with degrees k and m (resp.), with 0 ≤ m ≤ k − 1, such that pnk+m(x) = θm(x)qn(πk(x)) (n = 0, 1, 2, . . .). In...

Orthogonal Polynomials on Several Intervals via a Polynomial Mapping

Starting from a sequence {pn{x; no)} of orthogonal polynomials with an orthogonality measure yurj supported on Eo C [—1,1], we construct a new sequence {p„(x;fi)} of orthogonal polynomials on£ = T~1(Eq) (T is a polynomial of degree TV) with an orthogonality measure [i that is related to noIf Eo = [—1,1], then E = T_1([-l,l]) will in general consist of TV intervals. We give explicit formulas rel...

Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control

Optimal control problems for partial differential equation are often hard to tackle numerically because their discretization leads to very large scale optimization problems. Therefore, different techniques of model reduction were developed to approximate these problems by smaller ones that are tractable with less effort. Balanced truncation [2, 66, 81] is one well studied model reduction techni...

Model Reduction via Proper Orthogonal Decomposition

Multibody Grouping via Orthogonal Subspace Decomposition

Multibody structure f rom motion could be solved by the factorization approach. However, the noise measurements would make the segmentation daficult when analyzing the shape interaction matrix. This paper presents an orthogonal subspace decomposition and grouping technique t o approach such a problem. W e decompose the object shape spaces into signal subspaces and noise subspaces. W e show that...