C. F. Van Loan, Generalizing the singular value decomposition, SIAM J. Num. Anal., 13(1976), 76-83. 26  Home/Search Document Not in Database Summary Related Articles Check |
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A Jacobi Method for Computing Generalized Hyperbolic SVD - Bojanczyk (Correct)
....might be possible to extend these results to the GHSVD decomposition. Another issue not explicitly addressed in this note is the convergance of the Jacobi method when applied to the computation of the GHSVD. Convergance results for a related J symmetric Jacobi method were presented in [14] and [24] and should carry over to the case of the GHSVD. The case when the symmetric indefinite pencil (16) is not directly given in a factored form was recently addressed in [11] where a stable method for computing eigenvalues and eigenvectors was proposed. It is likely that the method developed in [11] ....
C. F. Van Loan. "Generalizing the singular value decomposition," SIAM J. Numer. Anal., 13 (1976), pp. 76--83.
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....is required to be orthogonal, then the best that can be done is to make #A and #B triangular. An appropriate choice of orthogonal X, VA , and VB guarantees that # 1 A #B will be diagonal. More generally, when A and B are possibly rank deficient m n a and m n b matrices, the generalized SVD [10, 13] has been defined by X 1 AV 1 = # #A 0 # r m r , X 1 BV 2 = # #B 0 # r m r , 1.1) where #A = # # I A SA 0A # # , #B = # # 0B SB I B # # # Received by the editors April 23, 1997; accepted for publication (in revised form) by L. Elden September 11, 1998; published ....
C. F. Van Loan, Generalizing the singular value decomposition, SIAM J. Numer. Anal., 13 (1976), pp. 76--83.
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.... ( 1 k DeltaH 1 k 2 2 k DeltaH 2 k 2 ) v u u t n X i=1 h p ( i ; e i ) i 2 2 Gamma1=p ( 1 k DeltaH 1 kF 2 k DeltaH 2 kF ) As to the scaled generalized singular value problem mentioned above, we shall consider instead its corresponding generalized eigenvalue problem [21, 36, 37] for S 1 G 1 G 1 S 1 Gamma S 2 G 2 G 2 S 2 and S 1 e G 1 e G 1 S 1 Gamma S 2 e G 2 e G 2 S 2 : 7.3) Theorem 7.3. Let fB 1 ; B 2 g j fG 1 S 1 ; G 2 S 2 g and f e B 1 ; e B 2 g j f e G 1 S 1 ; e G 2 S 2 g, where G 1 and G 2 are n Theta n and nonsingular and kG ....
C. F. Van Loan, Generalizing the singular value decomposition, SIAM Journal on Numerical Analysis, 13 (1976), pp. 76--83.
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C. F. Van Loan, Generalizing the singular value decomposition, SIAM J. Num. Anal., 13(1976), 76-83. 26
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C. F. Van Loan, Generalizing the singular value decomposition, SIAM J. Numer. Anal., 13(1976), 76-83.
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C. F. Van Loan. Generalizing the singular value decomposition. SIAM Journal on Numerical Analysis, 13:76--83, 1976.
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C.F. Van Loan, Generalizing the singular value decomposition. SIAM J. Numer. Anal. 13 (1976), pp. 76-83. 20
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C.F. Van Loan, Generalizing the singular value decomposition, SIAM J. Numer. Anal., 13 (1976), pp. 76-83.
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C. F. Van Loan. Generalizing the Singular Value Decomposition. SIAM Journal on Numerical Analysis, 13:76--83, 1976.
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C. F. Van Loan, Generalizing the singular value decomposition, SIAM J. Num. Anal., 13:76--83 (1976).
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C. F. Van Loan, Generalizing the singular value decomposition, SIAM Journal on Numerical Analysis, 13 (1976), pp. 76--83.
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