Approximation of an initial matrix by a Toeplitz one for acceleration of iterative solution of dense linear algebraic systems in scattering problems
Sergey P. Kuksenko, Talgat Rashitovich Gazizov, I. S. Kostarev · 2016
In iterative solution of linear algebraic systems, in order to accelerate matrix-vector multiplication by means of FFT usage, it is proposed to replace an initial matrix of a system with a Toeplitz matrix. Solution accuracy evaluation, relatively to the Gaussian elimination method, is presented. Results of usage of two BiCGStab method variants are demonstrated. The possibility to obtain up to 1.8 times speed-up (comparatively to the case without FFT acceleration) by the example of calculation of currents induced by external field in a conductive square plate is shown. An important trend of solution acceleration and accuracy increasing with increasing of N is revealed.