Determinant Expansions of Signed Matrices and of Certain Jacobians
This paper treats two topics: Matrices with sign patterns and Jacobians of certain mappings on the nonnegative orthant $\mathbb{R}_{\geq0}^d$. The main topic is counting the number of positive and ne...
This paper treats two topics: Matrices with sign patterns and Jacobians of certain mappings on the nonnegative orthant $\mathbb{R}_{\geq0}^d$. The main topic is counting the number of positive and ne...
Preconditioning of Boundary Value Problems Using Elementwise Schur Complements
This paper deals with an efficient technique for computing high-quality approximations of Schur complement matrices to be used in various preconditioners for the iterative solution of finite element ...
This paper deals with an efficient technique for computing high-quality approximations of Schur complement matrices to be used in various preconditioners for the iterative solution of finite element ...
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Matrix Cubes Parameterized by Eigenvalues
SIAM. J. Matrix Anal. & Appl. Volume 31, Issue 2, pp. 755-766 (2009)
Published June 26, 2009
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An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue functions on an affine space of symmetric matrices. A linear matrix inequality (LMI) representation is given for the convex set of all feasible instances, and its boundary is studied from the perspective of algebraic geometry. This generalizes the known LMI representations of $k$-ellipses and $k$-ellipsoids.
©2009 Society for Industrial and Applied Mathematics| History: | Received April 29, 2008; accepted April 15, 2009; published June 26, 2009 |
| Permalink: | http://dx.doi.org/10.1137/080722606 |
KEYWORDS and AMS
linear matrix inequality (LMI),
semidefinite programming (SDP),
matrix cube,
tensor product,
tensor sum,
$k$-ellipse,
algebraic degree
14P10, 34K20, 65K10, 90C22
PUBLICATION DATA
0895-4798 (print)
1095-7162 (online)
SIAM