The boundary curve of pseudospectrum and the stepsize control of curve tracing algorithm
The boundary curve of pseudospectrum and the stepsize control of curve tracing algorithm
Summary: The boundary curve of the pseudospectrum is defined as a contour line of its resolvent norm. The curve tracing algorithm is a rather simple continuation method, which determines this curve by a prediction-correction scheme. But this algorithm can not deal with the bifurcation point where the resolvent norm is not differentiable. Due to this defect we investigate the smoothness of the boundary curve, and give a method of stepsize control which can deal with bifurcation points. Numerical results are also presented.
Numerical computation of eigenvalues and eigenvectors of matrices, stepsize control, curve tracing algorithm, algorithm, continuation method, Numerical results, pseudospectrum, prediction-correction scheme, bifurcation point, Global methods, including homotopy approaches to the numerical solution of nonlinear equations
Numerical computation of eigenvalues and eigenvectors of matrices, stepsize control, curve tracing algorithm, algorithm, continuation method, Numerical results, pseudospectrum, prediction-correction scheme, bifurcation point, Global methods, including homotopy approaches to the numerical solution of nonlinear equations