Some new methods for the solution of matrix equations arising from discretized partial differential equations
Desmond J. Walton · Mspace (University of Manitoba) · 1978
The matrix equation XA+ÀY=F l. 2. 2 paEti:l-gllfeEglligr -eguatigns: partial 1ítferentiaL equations of the form (1.2.31 shef,e u (x,yl is known on the ttoundary of a qiven region" hève many aÐPlications in phYsical and enoineerinl problems (üvint.-Iri 5 1 I pages 201-2021 .Ricklev 'ìnd ucNamee [ 11 ] shós hor¿ f inri' e dirference iliscretization of equation (1.2"3) lelds to the natrLx eguation (1'1,|' The nunerical solution o.t some partlal differential equations are discussed in fuEther iletail in chaPteE 5. ll .2. I 3he-ss.!s.lggçg!s!-gg-!geÊÞc[ggr -o þ9s ger q* Assune that a plant has a single output v where t=Y!r v=gr!. and that the corEesPonaling observeE is driven by v as its on 1y input, then Z=-*Z+Þv, or 2=-xz+Þg's-Untter these conditions z = A! , chere À sati sfies (Luenberger [ 42 ]]X¡l + ÀY = Þc, , #,",0,, #(x,v) = r(x,v),