The family of general Jacobi polynomials P (α,β) n where α, β ∈ C can be characterised by complex (nonhermitian) orthogonality relations (cf. [15]). The special subclass of Jacobi polynomials P (α,β) n where α, β ∈ R are classical and the real orthogonality, quasi-orthogonality as well as related properties, such as the behaviour of the n real zeros, have been well studied. There is another spe...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

Zernike polynomials are an orthogonal set over a unit circle and are often used to represent surface distortions from FEA analyses. There are several reasons why these coefficients may lose their orthogonality in an FEA analysis. The effects, their importance, and techniques for identifying and improving orthogonality are discussed. Alternative representations are presented.

This paper presents a method for overcoming time-varying co-channel interference (CCI) using type-2 fuzzy adaptive filters (FAF). The type-2 FAF is realized using an unnormalized type-2 Takagi–Sugeno–Kang fuzzy logic system. A clustering method is used to adaptively design the parameters of the FAF. We use transversal equalizer and decision feedback equalizer structures to eliminate the CCI. Si...

For EDGE systems with transmit diversity in frequency-selective channels, the orthogonality of space time block coding (STBC) is ruined by the delay spreads of multipath channels and the interference is enhanced by the multi-antenna transmission respectively. The enhanced cochannel and co-antenna interference cannot be suppressed by the conventional equalization. In this paper a maximum likelih...

Relational clustering with heterogeneous data objects has impact in various important applications, such as web mining, text mining and bioinformatics etc. In this paper, we build a star-structured general model for relational clustering. It is formulated as an orthogonal tri-nonnegative matrix factorization. The model performs matrix approximation among all different data types to look for hid...

We generalize the array orthogonality property for perfect autocorrelation sequences to n-dimensional arrays. The generalized array orthogonality property is used to derive a number of ndimensional perfect array constructions.

We establish the orthogonality of the range and the kernel of a normal derivation with respect to the unitarily invariant norms associated with norm ideals of operators. Related orthogonality results for certain nonnormal derivations are also given.

Abs t rac t -P roper t i e s of nonlinear multiobjective problems implied by the Karush-Kuhn-Tucker necessary conditions are investigated. It is shown that trajectories of Lagrange multipliers corresponding to the components of the vector cost function are orthogonal to the corresponding trajectories of vector deviations in the balance space (to the balance set for Pareto solutions). ~) 2003 El...