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On Cones of Nonnegative Quadratic Functions

by Jos F. Sturm, Shuzhong Zhang, Hong Kong , 2001
"... We derive LMI-characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co-positivity. These matrix cones are in fact cones of non-convex quadratic functions that are nonnegative on a certain domain. As a domain, we consider for ..."
Abstract - Cited by 71 (15 self) - Add to MetaCart
We derive LMI-characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co-positivity. These matrix cones are in fact cones of non-convex quadratic functions that are nonnegative on a certain domain. As a domain, we consider

Quadratic functions

by Yung-yu Chuang, Slides Richard Szeliski, Steve Seitz, Marc Pollefyes
"... • Nonlinear least square methods ..."
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• Nonlinear least square methods

On the Stability of Quadratic Functional Equation

by Kanya Mahavidyalaya Kharkhoda (india
"... In this paper the stability of quadratic functional equation, f(xy)+f(xy-1)=2f(x)+2f(y) on class of groups is obtained and also prove that quadratic functional equation may not be stable in any abelian group. ..."
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In this paper the stability of quadratic functional equation, f(xy)+f(xy-1)=2f(x)+2f(y) on class of groups is obtained and also prove that quadratic functional equation may not be stable in any abelian group.

On the Estimation of Quadratic Functionals

by Jianqing Fan
"... We discuss the difficulties of estimating quadratic functionals based on observations Y (t) from the white noise model Y (t) = Jf (u)du + cr W (t), t E [0,1], o where W (t) is a standard Wiener process on [0, 1]. The optimal rates of convergence (as cr-> 0) for estimating quadratic functionals u ..."
Abstract - Cited by 38 (10 self) - Add to MetaCart
We discuss the difficulties of estimating quadratic functionals based on observations Y (t) from the white noise model Y (t) = Jf (u)du + cr W (t), t E [0,1], o where W (t) is a standard Wiener process on [0, 1]. The optimal rates of convergence (as cr-> 0) for estimating quadratic functionals

QUADRATIC FUNCTIONS ON TORSION GROUPS

by Florian Deloup, Gwénaël Massuyeau , 2003
"... A quadratic function q on an Abelian group G is a map, with values in an Abelian group, such that the map b: (x, y) ↦ → q(x + y) − q(x) − q(y) is Z-bilinear. Such a map q satisfies q(0) = 0. If, in addition, q satisfies the relation q(nx) = n 2 q(x) for all n ∈ Z and x ∈ G, then q is homogeneous ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
A quadratic function q on an Abelian group G is a map, with values in an Abelian group, such that the map b: (x, y) ↦ → q(x + y) − q(x) − q(y) is Z-bilinear. Such a map q satisfies q(0) = 0. If, in addition, q satisfies the relation q(nx) = n 2 q(x) for all n ∈ Z and x ∈ G, then q

On Cones of Nonnegative Quadratic Functions

by unknown authors , 2001
"... We derive LMI-characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co-positivity. These matrix cones are in fact cones of non-convex quadratic functions that are nonnegative on a certain domain. As a domain, we consider for ..."
Abstract - Add to MetaCart
We derive LMI-characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co-positivity. These matrix cones are in fact cones of non-convex quadratic functions that are nonnegative on a certain domain. As a domain, we consider

FUZZY ALMOST QUADRATIC FUNCTIONS

by A. K. Mirmostafaee, M. S. Moslehian , 710
"... Abstract. We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y). Our result can be regarded as a generalization of the stab ..."
Abstract - Cited by 9 (0 self) - Add to MetaCart
Abstract. We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y). Our result can be regarded as a generalization

On the Stability of Quadratic Functional Equations in -Spaces

by Xiuzhong Yang
"... The Hyers-Ulam-Rassias stability of quadratic functional equation (2 + ) + (2 − ) = ( + ) + ( − ) + 6 ( ) and orthogonal stability of the Pexiderized quadratic functional equation ( + ) + ( − ) = 2 ( ) + 2ℎ( ) in -spaces are proved. ..."
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The Hyers-Ulam-Rassias stability of quadratic functional equation (2 + ) + (2 − ) = ( + ) + ( − ) + 6 ( ) and orthogonal stability of the Pexiderized quadratic functional equation ( + ) + ( − ) = 2 ( ) + 2ℎ( ) in -spaces are proved.

Minimizing quadratic functions with separable

by R. Ku ˇcera , 2006
"... This article deals with minimizing quadratic functions with a special form of quadratic constraints that arise in 3D contact problems of linear elasticity with isotropic friction [Haslinger, J., Kučera, R. and Dostál, Z., 2004, An algorithm for the numerical realization of 3D contact problems with ..."
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This article deals with minimizing quadratic functions with a special form of quadratic constraints that arise in 3D contact problems of linear elasticity with isotropic friction [Haslinger, J., Kučera, R. and Dostál, Z., 2004, An algorithm for the numerical realization of 3D contact problems

Diagonalization Approach to Discrete Quadratic Functionals

by M. Bohner, O. Dosly, R. Hilscher, W. Kratz - ARCHIVES OF INEQUALITIES AND APPLICATIONS , 2003
"... A necessary and sufficient condition for the nonnegativity of the discrete quadratic functional corresponding to a symplectic difference system is proved using the diagonalization method. ..."
Abstract - Cited by 4 (2 self) - Add to MetaCart
A necessary and sufficient condition for the nonnegativity of the discrete quadratic functional corresponding to a symplectic difference system is proved using the diagonalization method.
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