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3 results

5 - Singular Supports
from Part One - Historical and Theoretical Background
Jean Bernard Lasserre, Edouard Pauwels, Institut de Recherche en Informatique, Toulouse, Mihai Putinar, University of California, Santa Barbara
Book:

The Christoffel–Darboux Kernel for Data Analysis

Published online:

31 March 2022

Print publication:

07 April 2022, pp 61-74
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Summary

Basic concepts and results of real and complex algebraic geometry enter into play when dealing with the estimation of measures supported by algebraic varieties. Some geometric constraints on the supporting variety are inherited from the very beginning of the modelization, such as a sphere for estimating an orientation in space. Well-adapted results of multivariate pluripotential theory play a crucial role here.

Controllability problems for the 1-D wave equation on ahalf-axis with the Dirichlet boundary control
Larissa V. Fardigola
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 18 / Issue 3 / July 2012

Published online by Cambridge University Press:

19 September 2011, pp. 748-773

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July 2012
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In this paper necessary and sufficient conditions of L∞-controllability andapproximate L∞-controllability are obtained for the control systemwtt = wxx − q2w,w(0,t) = u(t),x > 0, t ∈ (0,T), whereq ≥ 0, T > 0,u ∈ L∞(0,T) is a control. This system isconsidered in the Sobolev spaces.

Iterative methods for computing generalized inverses related with optimization methods
Part of
Dragan S. Djordjević, Predrag S. Stanimirović
Journal:

Journal of the Australian Mathematical Society / Volume 78 / Issue 2 / April 2005

Published online by Cambridge University Press:

09 April 2009, pp. 257-272

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April 2005
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We develop several iterative methods for computing generalized inverses using both first and second order optimization methods in C*-algebras. Known steepest descent iterative methods are generalized in C*-algebras. We introduce second order methods based on the minimization of the norms ‖Ax − b‖2 and ‖x‖2 by means of the known second order unconstrained minimization methods. We give several examples which illustrate our theory.

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3 results

5 - Singular Supports

Summary

Controllability problems for the 1-D wave equation on ahalf-axis with the Dirichlet boundary control

Iterative methods for computing generalized inverses related with optimization methods