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Hybrid Methods for Nonlinear Least Squares Problems
Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan
This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with extensive computational tests and comparisons of the introduced methods. All hybrid methods are described in detail and their global convergence is proved in a unified way. Some proofs concerning trust region methods, which are difficult to find in the literature, are also added. In particular, the report contains an analysis of a new simple hybrid method with Jacobian corrections (Section 8) and an investigation of the simple hybrid method for sparse least squares problems proposed previously in [33] (Section 14).
Plný tet: 0504615-av1 -  PDF
Plný text: content.csg - PDF
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Numerical solution of nonlinear transport problems
Bezchlebová, Eva ; Feistauer, Miloslav (vedoucí práce) ; Vlasák, Miloslav (oponent)
Práce je zaměřená na numerickou simulaci dvoufázového proudění. Je studován matematický model a numerická aproximace toku dvou nemísitelných nestlačitelných tekutin. Rozhraní mezi tekutinami je popsáno pomocí pomocí tzv. level set metody. Představena je diskretizace problému v prostoru a v čase. Metoda konečných prvk· se zpětnou Eulerovou metodou je aplikována na Navierovy-Stokesovy rovnice a časoprostorová nespojitá Galerkinova metoda je použita k řešení transportního problému. D·raz je kladen na analýzu chyby nespojité Galerkinovy metody přímek a časoprostorové nespojité Galerkinovy metody pro transportní problém. Jsou prezentovány numerické výsledky. 1
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A Modified Limited-Memory BNS Method for Unconstrained Minimization Derived from the Conjugate Directions Idea
Vlček, Jan ; Lukšan, Ladislav
A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization of the differentiable function $f:{\cal R}^N\to\cal R$ is considered, which consists in corrections (based on the idea of conjugate directions) of difference vectors for better satisfaction of the previous quasi-Newton conditions. In comparison with [11], more previous iterations can be utilized here. For quadratic objective functions, the improvement of convergence is the best one in some sense, all stored corrected difference vectors are conjugate and the quasi-Newton conditions with these vectors are satisfied. The algorithm is globally convergent for convex sufficiently smooth functions and our numerical experiments indicate its efficiency.
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Numerical experiments for turbulent flows
Trefilík, Jiří ; Kozel, Karel ; Příhoda, J.
The aim of the work is to explorethe possibilities of modelling transonic flowsin the internal and external aerodynamics. Several konfigurationswere analyzed and calculations were performed using both inviscid and viscous models of flow. Viscous turbulent flows have been simulated using either zero equation algebraic Baldwin-Lomax model and two equation k - w model in its basic version and improved TNT variant. The numerical solution was obtained using Lax-Wendroff scheme in the MAcCormack from on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability. Achieved results are compared with experimental data.
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