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A secant method for the matrix sign function
, 2009
"... A secant method for the matrix sign function ..."
A volumetric method for building complex models from range images,”
 in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM,
, 1996
"... Abstract A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, ..."
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Cited by 1020 (17 self)
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, and robustness in the presence of outliers. Prior algorithms possess subsets of these properties. In this paper, we present a volumetric method for integrating range images that possesses all of these properties. Our volumetric representation consists of a cumulative weighted signed distance function. Working
Using The Matrix Sign Function To Compute Invariant Subspaces
 SIAM J. Matrix Anal. Appl
, 1998
"... . The matrix sign function has several applications in system theory and matrix computations. However, the numericalbehavior of the matrix sign function, and its associated divideand conquer algorithm for computing invariant subspaces, are still not completely understood. In this paper, we present ..."
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Cited by 18 (1 self)
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. The matrix sign function has several applications in system theory and matrix computations. However, the numericalbehavior of the matrix sign function, and its associated divideand conquer algorithm for computing invariant subspaces, are still not completely understood. In this paper, we present
The Matrix Sign Function Method And The Computation Of Invariant Subspaces
 SIAM J. Matrix Anal. Applicat
, 1994
"... . A perturbation analysis shows that if a numerically stable procedure is used to compute the matrix sign function, then it is competitive with conventional methods for computing invariant subspaces. Stability analysis of the Newton iteration improves an earlier result of Byers and confirms that ill ..."
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Cited by 26 (5 self)
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. A perturbation analysis shows that if a numerically stable procedure is used to compute the matrix sign function, then it is competitive with conventional methods for computing invariant subspaces. Stability analysis of the Newton iteration improves an earlier result of Byers and confirms
The Generalized Newton Iteration for the Matrix Sign Function
, 1997
"... . In this paper we present modified algorithms for computing deflating subspaces of matrix pencils by means of the matrix sign function. Specifically, our new algorithms reduce the number of iterations to half, cut the cost of each Newton iteration by more than 50%, and improve the accuracy of the c ..."
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Cited by 3 (0 self)
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. In this paper we present modified algorithms for computing deflating subspaces of matrix pencils by means of the matrix sign function. Specifically, our new algorithms reduce the number of iterations to half, cut the cost of each Newton iteration by more than 50%, and improve the accuracy
Disk Functions And Their Relationship To The Matrix Sign Function
, 1997
"... This short paper investigates a generalization of the matrix sign function to matrix pencils. 1 Introduction The problem of extracting an invariant subspace of a matrix or a deflating subspace of a matrix pencil arises in many control computations including solving Lyapunov, Sylvester, and Riccati ..."
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Cited by 10 (7 self)
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This short paper investigates a generalization of the matrix sign function to matrix pencils. 1 Introduction The problem of extracting an invariant subspace of a matrix or a deflating subspace of a matrix pencil arises in many control computations including solving Lyapunov, Sylvester, and Riccati
Solving Stable Generalized Lyapunov Equations with the Matrix Sign Function
 NUMER. ALGORITHMS
, 1997
"... We investigate the numerical solution of the stable generalized Lyapunov equation via the sign function method. This approach has already been proposed to solve standard Lyapunov equations in several publications. The extension to the generalized case is straightforward. We consider some modificatio ..."
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Cited by 77 (40 self)
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We investigate the numerical solution of the stable generalized Lyapunov equation via the sign function method. This approach has already been proposed to solve standard Lyapunov equations in several publications. The extension to the generalized case is straightforward. We consider some
Numerical stability and instability in matrix sign function based algorithms
 Computational and Combinatorial Methods in Systems Theory
, 1986
"... This paper uses a forward and backward error analysis to try to identify some classes of matrices for . P which the matrix sign function is a numerically stable algorithm for extracting invariant subspaces roper scaling is essential to numerical stability as well as to rapid convergence. g a Roberts ..."
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Cited by 14 (5 self)
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This paper uses a forward and backward error analysis to try to identify some classes of matrices for . P which the matrix sign function is a numerically stable algorithm for extracting invariant subspaces roper scaling is essential to numerical stability as well as to rapid convergence. g a
Parallel Spectral Division Via The Generalized Matrix Sign Function
"... . In this paper we demonstrate the parallelism of the spectral division via the matrix sign function for the generalized nonsymmetric eigenproblem. We employ the socalled generalized Newton iterative scheme in order to compute the sign function of a matrix pair. A recent study has allowed considera ..."
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. In this paper we demonstrate the parallelism of the spectral division via the matrix sign function for the generalized nonsymmetric eigenproblem. We employ the socalled generalized Newton iterative scheme in order to compute the sign function of a matrix pair. A recent study has allowed
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