Z. Bai and J. W. Demmel, Using the matrix sign function to compute invariant subspaces, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 205--225. Home/Search Document Details and Download
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Large Scale Stabilization With Linear Feedback - Rao (1999) (Correct)
....both in discrete time and continuous time system, we have not discussed any useful method to compute continuous time unstable invariant subspace, especially for large scale system. The most recent method to compute continuous unstable invariant subspace of A is using the sign function of A (see [41] and references therein) The work of He and Mehrmann [8] combines projection via the sign function and a reduced order CRE that is transformed into an equivalent reduced order continuous time Lyapunov equation to stabilize continuous time system. 8.3 The Sign Function Method The sign function ....
Z. Bai and J. Demmel. Using the matrix sign function to compute invariant subspace. SIAM J. Matrix Anal. Appl., 19(1), 1998.
Solution of f(A)x=b with projection methods for the matrix A - van der Vorst (1999) (Correct)
....the matrix sign function one has to be extremely careful. A popular approach, based on a Newton iteration converges fast, but is sensitive for rounding errors, especially when A is ill conditioned. We will briefly discuss a computational method that was suggested (and analyzed) by Bai and Demmel [3]. This approach can also be combined, in principle, 2 Henk A. van der Vorst with the subspace reduction technique. Our early experiments, not reported here, indicate that the actual computation of approximate solutions of (1) is complicated because of the occurrence of the matrix B. Since this ....
....instance, the exp function of a matrix, as part of solution schemes for (parabolic) systems of equations. See, e.g. 10,8,11] Solution of f(A)x = b with projection methods for the matrix A 9 6 Matrix sign function The matrix sign function sign(A) for a nonsingular matrix A is defined as follows [3,13]. Let A = X diag(J ; J Gamma )X Gamma1 denote the decomposition of A 2 C n Thetan . The eigenvalues of J lie in the right half plane, and those of J Gamma are in the left half plane. Let I denote the identity matrix with the same dimensions as J , and I Gamma the identity matrix ....
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Bai, Z., Demmel, J.: Using the matrix sign function to compute invariant subspaces. SIAM J. Matrix Anal. Applic. 19 (1998) 205--225
Parallel Spectral Division Via The Generalized Matrix Sign.. - Huss-Lederman, al. (Correct)
.... subspaces are obtained by using a Schur deflation technique proposed in [21] Note that this subspace extraction only requires one generalized Newton iteration for computing both the left and right deflating subspaces and represents a reduction of 50 in the cost of previously proposed algorithms [2]. A variant of the generalized Newton iteration has been recently proposed in [22] which further reduces the cost. In this algorithm, GBNEWT, the matrix pair is initially transformed to the equivalent form (A0 ; B0 ) U T AV; BI ) here, U , V 2 C n Thetan are unitary matrices which reduce B ....
Z. Bai and J. Demmel. Using the matrix sign function to compute invariant subspaces. SIAM J. Matrix Anal. Appl., 19(1):205--225, 1998.
Computing The Polar Decomposition And The Matrix - Sign Decomposition In (Correct)
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Z. Bai and J. W. Demmel, Using the matrix sign function to compute invariant subspaces, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 205--225.
Implementation Aspects - For Eective Use (Correct)
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Z. Bai and J. W. Demmel. Using the matrix sign function to compute invariant subspaces. SIAM J. Matrix Anal. Applic., 1998:205--225, 1998.
Specialized Parallel Algorithms for Solving Linear Matrix.. - Quintana-Orti, Geijn (2000) (1 citation) (Correct)
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Z. Bai and J. Demmel. Using the matrix sign function to compute invariant subspaces. SIAMMatrix, 19(1):205--225, 1998.
Fast Parallel Kernels for Selected Problems in Control Theory - Quintana-Orti, Geijn (1999) (1 citation) (Correct)
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Z. Bai and J. Demmel. Using the matrix sign function to compute invariant subspaces. SIAM J. Matrix Anal. Appl., 19(1):205--225, 1998.
Parallel Solution of Selected Problems in Control Theory - Quintana-Orti, Geijn (1998) (Correct)
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Z. Bai and J. Demmel. Using the matrix sign function to compute invariant subspaces. SIAMMatrix, 19(1):205--225, 1998.
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