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DETERMINANT MAXIMIZATION WITH LINEAR MATRIX INEQUALITY CONSTRAINTS
"... The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the s ..."
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Cited by 183 (18 self)
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The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the semidefinite programming problem. We give an overview of the applications of the determinant maximization problem, pointing out simple cases where specialized algorithms or analytical solutions are known. We then describe an interiorpoint method, with a simplified analysis of the worstcase complexity and numerical results that indicate that the method is very efficient, both in theory and in practice. Compared to existing specialized algorithms (where they are available), the interiorpoint method will generally be slower; the advantage is that it handles a much wider variety of problems.
A Schur Method for LowRank Matrix Approximation
, 1996
"... This paper describes a much simpler generalized Schurtype algorithm to compute similar lowrank approximants. For a given matrix H which has d singular values larger than e, we find all rank d approximants H such that ..."
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Cited by 21 (8 self)
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This paper describes a much simpler generalized Schurtype algorithm to compute similar lowrank approximants. For a given matrix H which has d singular values larger than e, we find all rank d approximants H such that
On The HankelNorm Approximation Of UpperTriangular Operators And Matrices
 INTEGRAL EQUATIONS AND OPERATOR THEORY
, 1993
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On LowComplexity Approximation of Matrices
 Lin. Alg. Appl
, 1992
"... this paper, we pursue a complementary notion of structure which we will call the state structure. The state structure applies to upper triangular matrices and is seemingly unrelated to the Toeplitz or displacement structure mentioned above. A first purpose of the computational schemes considered in ..."
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Cited by 4 (3 self)
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this paper, we pursue a complementary notion of structure which we will call the state structure. The state structure applies to upper triangular matrices and is seemingly unrelated to the Toeplitz or displacement structure mentioned above. A first purpose of the computational schemes considered in this paper is to perform a desired linear transformation T on some vector (`input sequence')
Modeling Computational Networks By TimeVarying Systems
, 1993
"... Many computational schemes in linear algebra can be studied from the point of view of (discrete) timevarying linear systems theory. For example, the operation `multiplication of a vector by an upper triangular matrix' can be represented by a computational scheme (or model) that acts sequentiall ..."
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Many computational schemes in linear algebra can be studied from the point of view of (discrete) timevarying linear systems theory. For example, the operation `multiplication of a vector by an upper triangular matrix' can be represented by a computational scheme (or model) that acts sequentially on the entries of the vector. The number of intermediate quantities (`states') that are needed in the computations is a measure of the complexity of the model. If the matrix is large but its complexity is low, then not only multiplication, but also other operations such as inversion and factorization, can be carried out efficiently using the model rather than the original matrix. In the present paper we discuss a number of techniques in timevarying system theory that can be used to capture a given matrix into such a computational network. Keywords: computational linear algebra models, model reduction, fast matrix algorithms. 1. INTRODUCTION 1.1. Computational linear algebra and timevarying m...
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS (REVISED) 1 Comparative Study of JointDetection Techniques for TDCDMA based Mobile Radio Systems
"... Third generation mobile radio systems use TDCDMA in their TDD mode. Due to the TDMA component of TDCDMA, joint (or multiuser) detection techniques can be implemented with a reasonable complexity. Therefore, joint detection will already be implemented in the first phase of the system deployment to ..."
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Third generation mobile radio systems use TDCDMA in their TDD mode. Due to the TDMA component of TDCDMA, joint (or multiuser) detection techniques can be implemented with a reasonable complexity. Therefore, joint detection will already be implemented in the first phase of the system deployment to eliminate the intracell interference. In a TDCDMA mobile radio system, jointdetection is performed by solving a least squares problem, where the system matrix has a blockSylvester structure. In this paper, we present and compare several techniques that reduce the computational complexity of the joint detection task even further by exploiting this blockSylvester structure and by incorporating different approximations. These techniques are based on the Cholesky factorization, the Levinson algorithm, the Schur algorithm, and on Fourier techniques, respectively. The focus of this paper is on Fourier techniques since they have the smallest computational complexity and achieve the same performance as the joint detection algorithm that does not use any approximations. Similar to the wellknown implementation of fast convolutions, the resulting Fourierbased joint detection scheme also uses a sequence of FFTs and overlapping. It is well suited for the implementation on parallel hardware architectures.