"5"^^ . "0029-5981" . "Markopoulos, Alexandros" . . "[058D5B1EB8D5]" . . . . "5"^^ . . "5" . . "Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure"@en . "The direct methods for the solution of systems of linear equations with a symmetric positive semidefinite matrix A usually comprise the Cholesky decomposition of a nonsingular diagonal block of A and effective evaluation of the action of a generalized inverse of the corresponding Schur complement. In this note we deal with both problems, paying special attention to the stiffness matrices of floating structures without mechanisms. We present a procedure which first identifies a well-conditioned positive definite diagonal block, then decomposes it by the Cholesky decomposition, and finally evaluates a generalized inverse of the Schur complement S. The Schur complement is typically very small, so the generalized inverse can be effectively evaluated by the SVD. If the rank of A or a lower bound on the nonzero eigenvalues of A are known, then the SVD can be implemented without any ``epsilon'. Moreover, if the kernel of A is known, then the SVD can be replaced by effective regularization. The results of numerical experiments show that the proposed method is useful for effective implementation of the FETI based domain decomposition methods." . "domain decomposition; generalized inverse; semidefinite matrices; Cholesky decomposition"@en . "RIV/61989100:27240/11:86080658" . "88" . . "Dost\u00E1l, Zden\u011Bk" . "The direct methods for the solution of systems of linear equations with a symmetric positive semidefinite matrix A usually comprise the Cholesky decomposition of a nonsingular diagonal block of A and effective evaluation of the action of a generalized inverse of the corresponding Schur complement. In this note we deal with both problems, paying special attention to the stiffness matrices of floating structures without mechanisms. We present a procedure which first identifies a well-conditioned positive definite diagonal block, then decomposes it by the Cholesky decomposition, and finally evaluates a generalized inverse of the Schur complement S. The Schur complement is typically very small, so the generalized inverse can be effectively evaluated by the SVD. If the rank of A or a lower bound on the nonzero eigenvalues of A are known, then the SVD can be implemented without any ``epsilon'. Moreover, if the kernel of A is known, then the SVD can be replaced by effective regularization. The results of numerical experiments show that the proposed method is useful for effective implementation of the FETI based domain decomposition methods."@en . . "Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure" . "RIV/61989100:27240/11:86080658!RIV13-GA0-27240___" . . . "000295226800004" . . . "10.1002/nme.3187" . "Kozubek, Tom\u00E1\u0161" . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . . "INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING" . . . "P(GA201/07/0294), Z(MSM6198910027)" . . . "Brzobohat\u00FD, Tom\u00E1\u0161" . . "Kov\u00E1\u0159, Petr" . . "Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure" . "190258" . . "17"^^ . "27240" . . . . "Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure"@en .