Title :
Symmetric polynomials in the transfer matrix scaling
Author :
Belyayev, Yuriy N.
Author_Institution :
Syktyvkar Univ., Syktyvkar, Russia
Abstract :
The new method of the matrix exponential exp (Wz) computation is based on the use of symmetric polynomials of n-th order in combination with scaling matrix W. Calculation algorithm uses a new type of recurrence relations, which were obtained for symmetric polynomials. Evaluation of the scaling parameter, which provides a reliable calculation of the matrix exponential with admissible truncation error, is made. Method of minimizing roundoff errors in the calculation of high powers of matrices is suggested.
Keywords :
error analysis; matrix algebra; polynomials; wave propagation; calculation algorithm; matrix exponential exp computation; roundoff errors; scaling matrix; symmetric polynomials; transfer matrix scaling; truncation error; wave propagation; Chebyshev approximation; Diffraction; Finite wordlength effects; Matrix decomposition; Polynomials; Symmetric matrices;
Conference_Titel :
Days on Diffraction (DD), 2013
Conference_Location :
St. Petersburg
Print_ISBN :
978-1-4799-1037-3
DOI :
10.1109/DD.2013.6712796