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Orthogonal Polynomials of Several Variables
 Encyclopedia of Mathematics and its Applications
, 2001
"... Abstract. We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation. 1 ..."
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Cited by 232 (44 self)
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Abstract. We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation. 1
IN SEVERAL VARIABLES
, 2003
"... Abstract. For a convex, real function f we present a simple proof of the formula Tr(f ( ∑m k=1 a ∗ kxkak)) ≤ Tr ( ∑m k=1 a ∗ kf(xk)ak), valid for each tuple (x1,..., xm) of symmetric matrices in Mn and every unital column (a1,..., am) of matrices, i.e. ∑m k=1 a ∗ kak = 1. This is the standard Jense ..."
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Cited by 11 (0 self)
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Jensen trace inequality. If f ≥ 0 it holds also for the unbounded trace on B(H), where H is an infinitedimensional Hilbert space. We then investigate the more general case where τ is a densely defined, lower semicontinuous trace on a C∗−algebra A and f is a convex, continuous function of n variables
STOLARSKY MEANS OF SEVERAL VARIABLES
, 2005
"... Communicated by Zs. Páles ABSTRACT. A generalization of the Stolarsky means to the case of several variables is presented. The new means are derived from the logarithmic mean of several variables studied in [9]. Basic properties and inequalities involving means under discussion are included. Limit t ..."
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Communicated by Zs. Páles ABSTRACT. A generalization of the Stolarsky means to the case of several variables is presented. The new means are derived from the logarithmic mean of several variables studied in [9]. Basic properties and inequalities involving means under discussion are included. Limit
Polynomial interpolation in several variables
, 2000
"... This is a survey of the main results on multivariate polynomial interpolation in the last twentyfive years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique inter ..."
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Cited by 71 (6 self)
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This is a survey of the main results on multivariate polynomial interpolation in the last twentyfive years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique interpolation for given interpolation spaces as well as the converse. In addition, one section is devoted to error formulas and another to connections with computer algebra. An extensive list of references is also included.
An introduction to variable and feature selection
 Journal of Machine Learning Research
, 2003
"... Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available. ..."
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Cited by 1283 (16 self)
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Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available.
Notes on series in several variables
"... These notes are elementary derivations of wellknown, but sometimes hard to find, facts on series in several variables. By "elementary " I mean "avoiding the theory of complex differentiation and integration, " and the basic ideas of the proofs will be natural gen ..."
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These notes are elementary derivations of wellknown, but sometimes hard to find, facts on series in several variables. By "elementary " I mean "avoiding the theory of complex differentiation and integration, " and the basic ideas of the proofs will be natural
Polynomials of Several Variables
, 2002
"... We consider the set σP of the power nonnegative polynomials of several variables.By QP we denote the class of the polynomials from σ1 which can be represented as a sum of squares.It is shown in the classic work by D.Hilbert[3] that QP does not coincide with σP.Step by step a number of polynomials ..."
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We consider the set σP of the power nonnegative polynomials of several variables.By QP we denote the class of the polynomials from σ1 which can be represented as a sum of squares.It is shown in the classic work by D.Hilbert[3] that QP does not coincide with σP.Step by step a number of polynomials
QUASISUMS IN SEVERAL VARIABLES
"... Abstract. In this note we introduce the notions of quasisums and of the local quasisums in several variables, respectively. We prove that the local quasisums are also quasisums. We show how this result can be applied to find the continuous solutions of the functional equation g(u11 + · · ·+ u1N ..."
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Abstract. In this note we introduce the notions of quasisums and of the local quasisums in several variables, respectively. We prove that the local quasisums are also quasisums. We show how this result can be applied to find the continuous solutions of the functional equation g(u11 + · · ·+ u1
Large margin methods for structured and interdependent output variables
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary ..."
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Cited by 612 (12 self)
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the complementary issue of designing classification algorithms that can deal with more complex outputs, such as trees, sequences, or sets. More generally, we consider problems involving multiple dependent output variables, structured output spaces, and classification problems with class attributes. In order
Results 1  10
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