Such relations are thus derived for certain symmetric sixrowed determinants. DQ, however, is of a highly specialized type ; it is the discriminant of the sum of three 6-ary squares. Is the relation (2), established for this special type, valid for all symmetric determinants of six rows ? It is ; for it involves no constituent from the principal diagonal, so that the 18 parameters of our 6 x 3 a...

A new constantWD(X) is introduced into any real 2n-dimensional symmetric normed space X . By virtue of this constant, an upper bound of the geometric constant D(X), which is used to measure the difference between Birkhoff orthogonality and isosceles orthogonality, is obtained and further extended to an arbitrarym-dimensional symmetric normed linear space (m≥ 2). As an application, the result is...

Takagi factorization or symmetric singular value decomposition is a special form of SVD applicable to symmetric complex matrices. The computation takes advantage of symmetry to reduce computation and storage requirements. The Jacobi method with chess tournament ordering was used to perform the computation in parallel on a GPU using the CUDA programming model. We were able to achieve speedups of...

An invariant theoretic characterization of subdiscriminants of matrices is given. The structure as a module over the special orthogonal group of the minimal degree non-zero homogeneous component of the vanishing ideal of the variety of real symmetric matrices with a bounded number of different eigenvalues is investigated. These results are applied to the study of sum of squares presentations of...

In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semidefinite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimizati...

We consider the extension of primal dual interior point methods for linear programming on symmetric cones, to a wider class of problems that includes approximate necessary optimality conditions for functions expressible as the difference of two convex functions of a special form. Our analysis applies the Jordan-algebraic approach to symmetric cones. As the basic method is local, we apply the id...

In this paper, a new pair of Mond-Weir type multiobjective second-order symmetric dual models with cone constraints is formulated in which the objective function is optimised with respect to an arbitrary closed convex cone. Usual duality relations are further established under K-η-bonvexity/second-order symmetric dual K-H-convexity assumptions. A nontrivial example has also been illustrated to ...

Spectra of the second derivative operators corresponding to the special PT -symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT -symmetric point interactions causing unusual spectral effects are investigated for the systems defined on a finite interval as well. The spectrum of this type of interactions is very far from the ...

In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semidefinite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimizati...

We are concerned with eigenvalue problems for definite and indefinite symmetric matrix pencils. First, Rayleigh-Ritz methods are formulated and, using Krylov subspaces, a convergence analysis is presented for definite pencils. Second, generalized symmetric Lanczos algorithms are introduced as a special Rayleigh-Ritz method. In particular, an a posteriori convergence criterion is demonstrated by...