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Víceúrovňové hierarchické předpodmínění (úvod do problematiky)
Blaheta, Radim ; Byczanski, Petr
The paper describes hierarchical decompositions and AMLI preconditioners, analysis of hierarchical decomposition methods through CBS constant in 2D and 3D, discusses robustness with respect to anisotropy and element shape and introduces fully algebraic AMLI with aggregation or agglomeration. Finally, the paper discusses recent results concerning algebraic theory of AMLI for nonconforming FEś.
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Parallel Computing and FEM
Blaheta, Radim
The contribution describes application of parallel computing for numerical solution of boundary value problems like elasticity, heat conduction etc. by the finite element method (FEM). The main application concerns solution of large scale linear algebraic systems by domain decomposition methods.
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Nonlinear models of suspension bridges
Malík, Josef
Some results concerning the geometric nonlinearity connected with torsion and bending of a road bed is analyzed. The basic nonlinear variational equations derived from principle of minimum energy are proposed.
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Lanczošova třídiagonalizace, Golub-Kahanova bidiagonalizace a core problém
Hnětynková, Iveta ; Strakoš, Zdeněk
Consider an orthogonally invariant linear approximation problem Ax ~ b. In "C.C. Paige, Z. Strakoš: Core problems in linear algebraic systems (SIAM J. Matrix Anal. Appl. 27 (2006), pp. 861-875)" it was proved that the partial upper bidiagonalization of the matrix [b,A] determines a core approximation problem that contains the necessary and sufficient information for solving the original problem. Our contribution derives the fundamental characteristics of the core problem from the known relationship between the Golub-Kahan bidiagonalization, the Lanczos tridiagonalization and the properties of Jacobi matrices.
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