On Spectral Approximation of Linear Operators

AbstractRefined error estimates are obtained for the approximation of discrete spectra of linear operators. It also provides an alternative approach to spectral approximation

Spectral Refinements of Newton Type for Eigenelements of Bounded Linear Operators

AbstractA theoretical framework is developed for constructing spectral refinement schemes for a simple eigenelement which achieve arbitrarily high rates of convergence while keeping the computational cost at a minimum. The new approach is illustrated by considering a Newton type iteration scheme. Numerical results are given by considering a model problem

Pseudospectra, critical points and multiple eigenvalues of matrix polynomials

AbstractWe develop a general framework for perturbation analysis of matrix polynomials. More specifically, we show that the normed linear space Lm(Cn×n) of n-by-n matrix polynomials of degree at most m provides a natural framework for perturbation analysis of matrix polynomials in Lm(Cn×n). We present a family of natural norms on the space Lm(Cn×n) and show that the norms on the spaces Cm+1 and Cn×n play a crucial role in the perturbation analysis of matrix polynomials. We define pseudospectra of matrix polynomials in the general framework of the normed space Lm(Cn×n) and show that the pseudospectra of matrix polynomials well known in the literature follow as special cases. We analyze various properties of pseudospectra in the unified framework of the normed space Lm(Cn×n). We analyze critical points of backward errors of approximate eigenvalues of matrix polynomials and show that each critical point is a multiple eigenvalue of an appropriately perturbed polynomial. We show that common boundary points of components of pseudospectra of matrix polynomials are critical points. As a consequence, we show that a solution of Wilkinson’s problem for matrix polynomials can be read off from the pseudospectra of matrix polynomials

Perturbation theory for Hamiltonian matrices and the distance to bounded-realness

Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple eigenvalues with mixed sign characteristics, which are then moved from the imaginary axis to specific locations in the complex plane by small Hamiltonian perturbations. We also present a numerical method to compute upper bounds for the minimal perturbations that move all eigenvalues of a given Hamiltonian matrix outside a vertical strip along the imaginary axis

Assessment of in-vivo anti-diabetic and anti-diarrheal effects of Flemingia stricta Roxb. leaf

The objective of this study was to evaluate the anti-diabetic and anti-diarrheal activity of methanol extract of Flemingia stricta Roxb. (Fabaceae) leaf. In anti-diabetic study, the extract was administered to alloxan-induce diabetic mice at two concentrations (200 mg/kg and 400 mg/kg body weight) for acute (12 hours) and prolong treatments (15 days) and blood glucose levels of diabetic mice were monitored at intervals of hours and days throughout the duration of treatment. Antidiarrheal test was conducted by castor oil induced diarrhea and enteropooling as well as intestinal motility in mice at three different concentration (100 mg/kg, 200 mg/kg and 400 mg/kg body weight). Treatment of alloxan induce diabetic mice with the extract caused a significant reduction in fasting blood glucose level of the diabetic mice both in acute (12 hours) and prolong treatment (15 days) and it was determined that the F. stricta methanol extract at both concentration (200 mg/kg and 400 mg/kg) showed the significant (P<0.05) hypoglycemic effect in comparison to the standard drug metformin. In the case of castor oil induced diarrheal test, enteropooling test and gastrointestinal motility test, the extract of F. stricta  at 100 mg/kg, 200 mg/kg and 400 mg/kg has given significant effect (P<0.05) compared to the standard drug loperamide. But 400 mg/kg demonstrated the highest activity amongst the three doses. These results suggested that the methanol extract of F. stricta Roxb. possess promising anti-diabetic effect on alloxan-induced mice and significant antidiarrheal effect on castor oil induced diarrheal mice. DOI: http://dx.doi.org/10.5281/zenodo.383974