Orthogonal similarity transformation into block-semiseparable matrices of semiseparability rankk

2005 ◽  
Vol 12 (10) ◽  
pp. 981-1000 ◽  
Author(s):  
M. Van Barel ◽  
E. Van Camp ◽  
N. Mastronardi
Keyword(s):  
Similarity Transformation ◽  
Semiseparable Matrices ◽  
Orthogonal Similarity Transformation

scholarly journals Решение обратной задачи для сложного вибронного аналога резонанса Ферми на основе плоских вращений Якоби

2020 ◽  
Vol 128 (11) ◽  
pp. 1614
Author(s):  
В.А. Кузьмицкий
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Data ◽  
Similarity Transformation ◽  
Accurate Solution ◽  
Fermi Resonance ◽  
Matrix Elements ◽  
Second Stage ◽  
The Matrix ◽  
Two Stages ◽  
Orthogonal Similarity Transformation

Based on algebraic methods, we have found an accurate solution for the inverse task for the vibronic analogue of the complex Fermi resonance, i.e. the determination from the spectral data (energies Ek and transition intensities Ik of the observed conglomerate of lines, k = 1, 2, ..., n; n > 2) energies of the «dark» states Am and the matrix elements of their coupling Bm with the «bright» state. The algorithm consists of two stages. At the first stage, the Jacobi plane rotations are used to construct an orthogonal similarity transformation matrix X, for which the elements of the first row obey the requirement (X1k)^2 = Ik, which corresponds to that fact that there is only one non-perturbed «bright» state. At the second stage, the quantities Am and Bm are obtained after solving the eigenvalue problem for block of «dark» states of the matrix Xdiag({Ek})X-1.

IMPROVED DETECTION OF BIFURCATIONS IN LARGE NONLINEAR SYSTEMS VIA THE CONTINUATION OF INVARIANT SUBSPACES ALGORITHM

2001 ◽  
Vol 11 (08) ◽  
pp. 2277-2285 ◽  
Author(s):  
M. J. FRIEDMAN
Keyword(s):  
Nonlinear Systems ◽  
Similarity Transformation ◽  
Invariant Subspaces ◽  
Iterative Refinement ◽  
Test Functions ◽  
Triangular Form ◽  
Reliable Detection ◽  
Parameter Dependent ◽  
Orthogonal Similarity Transformation

The Continuation of Invariant Subspaces (CIS) algorithm [Demmel et al., 2001; Dieci & Friedman, 2001] produces a smooth orthogonal similarity transformation to block triangular form of a parameter dependent matrix A(s). The CIS algorithm is an adaptation of an iterative refinement technique for improving the accuracy of computed invariant subspaces. On the basis of the CIS algorithm, new test functions are defined for an improved, more reliable detection of bifurcations in problems with simple bifurcations near multiple bifurcations, problems with multiple bifurcations, and problems with symmetries. Illustrative examples are given.

scholarly journals Flow towards a Stagnation Region of a Vertical Plate in a Hybrid Nanofluid: Assisting and Opposing Flows

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 448
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Radiation Effects ◽  
Vertical Plate ◽  
Similarity Transformation ◽  
Fluid Motion ◽  
Hybrid Nanoparticles ◽  
Problem Solver ◽  
Hybrid Nanofluid ◽  
Al2o3 Nanoparticles ◽  
Nanofluid Flow ◽  
Stagnation Region

This study investigates a hybrid nanofluid flow towards a stagnation region of a vertical plate with radiation effects. The hybrid nanofluid consists of copper (Cu) and alumina (Al2O3) nanoparticles which are added into water to form Cu-Al2O3/water nanofluid. The stagnation point flow describes the fluid motion in the stagnation region of a solid surface. In this study, both buoyancy assisting and opposing flows are considered. The similarity equations are obtained using a similarity transformation and numerical results are obtained via the boundary value problem solver (bvp4c) in MATLAB software. Findings discovered that dual solutions exist for both opposing and assisting flows. The heat transfer rate is intensified with the thermal radiation (49.63%) and the hybrid nanoparticles (32.37%).

A similarity transformation for a turbulent spot in a laminar boundary layer

1980 ◽  
Vol 23 (12) ◽  
pp. 2561 ◽  
Author(s):  
M. Sokolov ◽  
R. A. Antonia ◽  
A. J. Chambers
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Similarity Transformation ◽  
Turbulent Spot
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