Geodesic
Synthesis of a rational filter in the presence of complete alternance
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 6, pp. 921-933

Voir la notice de l'article provenant de la source Math-Net.Ru

The construction of a rational function that is nonnegative on two intervals of which one is infinite is considered. It is assumed that the maximum deviation of the function from zero on the infinite interval takes the minimum possible value under the condition that the values of the function on the finite interval are within the given bounds. It is assumed that the rational function (fraction) has the complete alternance. In this case, the original problem is reduced to solving a system of nonlinear equations. For solving this system, a two-stage method is proposed. At the first stage, a subsystem is selected and used to find a good approximation for the complete system. At the second stage, the complete system of nonlinear equations is solved. The solution is explained in detail for the case when the order of the fraction is between one and four. Numerical results for a fraction of order ten are presented. 
@article{ZVMMF_2017_57_6_a1,
     author = {V. N. Malozemov and G. Sh. Tamasyan},
     title = {Synthesis of a rational filter in the presence of complete alternance},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {921--933},
     publisher = {mathdoc},
     volume = {57},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a1/}
}
TY  - JOUR
AU  - V. N. Malozemov
AU  - G. Sh. Tamasyan
TI  - Synthesis of a rational filter in the presence of complete alternance
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 921
EP  - 933
VL  - 57
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a1/
LA  - ru
ID  - ZVMMF_2017_57_6_a1
ER  - 
%0 Journal Article
%A V. N. Malozemov
%A G. Sh. Tamasyan
%T Synthesis of a rational filter in the presence of complete alternance
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 921-933
%V 57
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a1/
%G ru
%F ZVMMF_2017_57_6_a1
V. N. Malozemov; G. Sh. Tamasyan. Synthesis of a rational filter in the presence of complete alternance. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 6, pp. 921-933. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a1/