Quaternion polynomial matrix diagonalization for the separation of polarized convolutive mixture

2010 ◽  
Vol 90 (7) ◽  
pp. 2219-2231 ◽  
Author(s):  
Giovanni M. Menanno ◽  
Nicolas Le Bihan
Keyword(s):  
Polynomial Matrix ◽  
Convolutive Mixture ◽  
Matrix Diagonalization

CASE STUDY OF THE CONVERGENCY OF NONLINEAR PERTURBATION SERIES: MORSE–FESHBACH NONLINEAR SERIES

1999 ◽  
Vol 14 (13) ◽  
pp. 2103-2115 ◽  
Author(s):  
BISWANATH RATH
Keyword(s):  
New York ◽  
Energy Levels ◽  
Perturbation Series ◽  
Nonlinear Perturbation ◽  
Theoretical Physics ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
Divergent Behavior

We study the divergent behavior of the Morse–Feshbach nonlinear perturbation series (MFNS) [P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953)] for producing convergent energy levels using the ground state of a quartic anharmonic oscillator (AHO) in the strong coupling limit. Numerical calculations have been done up to tenth order. Further comparison of the MFNS convergent result has been made with the matrix diagonalization method.

scholarly journals Comparison of methods for solving the vibrational Schrödinger equation in the course of sequential Monte-Carlo-quantum mechanical treatment of hydroxide ion hydration

2010 ◽  
Vol 29 (2) ◽  
pp. 203
Author(s):  
Jasmina Petreska ◽  
Ljupco Pejov
Keyword(s):  
Sequential Monte Carlo ◽  
Reference Method ◽  
Hamiltonian Matrix ◽  
Ion Hydration ◽  
Hydroxide Ion ◽  
Frequency Shifts ◽  
One Dimensional ◽  
Quantum Mechanical Treatment ◽  
Wide Range ◽  
Matrix Diagonalization

Three numerical methods were applied to compute the anharmonic O–H stretching vibrational frequencies of the free and aqueous hydroxide ion on the basis of one-dimensional vibrational potential energies computed at various levels of theory: i) simple Hamiltonian matrix diagonalization technique, based on representation of the vibrational potential in Simons-Parr-Finlan (SPF) coordinates, ii) Numerov algorithm and iii) Fourier grid Hamiltonian method (FGH).Considering the Numerov algorithm as a reference method, the diagonalization technique performs remarkably well in a very wide range of frequencies and frequency shifts (up to 300 cm–1). FGH method, on the other hand, though showing a very good performance as well, exhibits more significant (and non-uniform) discrepancies with the Numerov algorithm, even for rather modest frequency shifts.

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