In this paper, we further generalize the technique for constructing the normal (or positive definite) and skew-Hermitian splitting iteration method for solving large sparse nonHermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove th...

Hyperbolic matrix polynomials are an important class of Hermitian matrix poly-nomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that their eigenvalues are real and semisimple. We extend the definition of hyperbolic matrix polynomial in a way that relaxes the requirement of definiteness of the leading coefficient matrix, yielding...

be a positive definite quadratic form with determinant D R and integer coefficients a ;Call it an even form if all a ; ; are even ., an odd form if at least one a ;; is odd . Then Í,, is called non-decomposable, if it cannot be expressed as a sum of two non-negative quadratic forms with integer coefficients . Mordell 1 ) proved that f, can always be decomposed into a sum of five squares of line...

The quality of a search engine is typically evaluated using hand-labeled data sets, where the labels indicate the relevance of documents to queries. Often the number of labels needed is too large to be created by the best annotators, and so less accurate labels (e.g. from crowdsourcing) must be used. This introduces errors in the labels, and thus errors in standard precision metrics (such as P@...