singular matrix- integral
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From: Magdalena Moczydlowska on 14 May 2010 03:57 You have right and this is simple. Thank You! But the second problem is how to calculate Int_{0}^{h} ( exp(h- s)A ) ds . The same integral but without A. Magdalena
From: Magdalena Moczydlowska on 14 May 2010 04:10 On 14 Maj, 09:57, Magdalena Moczydlowska <magdamoczydlow...(a)gmail.com> wrote: > You have right and this is simple. Thank You! > > But the second problem is how to calculate Int_{0}^{h} ( exp(h- > s)A ) ds . The same integral but without A. > > Magdalena Of course the assumption about A are the same as in the first message.
From: Rob Johnson on 14 May 2010 07:11 In article <cce824e6-0270-404f-b8fa-ba6abc5b2085(a)k17g2000yqf.googlegroups.com>, Magdalena Moczydlowska <magdamoczydlowska(a)gmail.com> wrote: >On 14 Maj, 09:57, Magdalena Moczydlowska <magdamoczydlow...(a)gmail.com> >wrote: >> You have right and this is simple. Thank You! >> >> But the second problem is how to calculate Int_{0}^{h} ( exp(h- >> s)A ) ds . The same integral but without A. >> >> Magdalena > >Of course the assumption about A are the same as in the first message. Consider the function E(x) = (exp(x)-1)/x. What is the derivative of tE(tA) with respect to t? Rob Johnson <rob(a)trash.whim.org> take out the trash before replying to view any ASCII art, display article in a monospaced font
From: Magdalena Moczydlowska on 14 May 2010 08:42 On 14 Maj, 13:11, r...(a)trash.whim.org (Rob Johnson) wrote: > In article <cce824e6-0270-404f-b8fa-ba6abc5b2...(a)k17g2000yqf.googlegroups..com>, > > Magdalena Moczydlowska <magdamoczydlow...(a)gmail.com> wrote: > >On 14 Maj, 09:57, Magdalena Moczydlowska <magdamoczydlow...(a)gmail.com> > >wrote: > >> You have right and this is simple. Thank You! > > >> But the second problem is how to calculate Int_{0}^{h} ( exp(h- > >> s)A ) ds . The same integral but without A. > > >> Magdalena > > >Of course the assumption about A are the same as in the first message. > > Consider the function E(x) = (exp(x)-1)/x. What is the derivative of > tE(tA) with respect to t? > > Rob Johnson <r...(a)trash.whim.org> > take out the trash before replying > to view any ASCII art, display article in a monospaced font It is -1+exp(tA)+A exp(At)/ tA but A is not inverible
From: George Jefferson on 14 May 2010 17:47
"Magdalena Moczydlowska" <magdamoczydlowska(a)gmail.com> wrote in message news:53a23e8d-0167-4c7d-8315-f5aa06439eb6(a)g21g2000yqk.googlegroups.com... > Hi! > > I have one question about the specific integral. > Assume that A is singular so it is not invertible ( we also kno that A > is stiff and semi-definite matrix so ||e^{hA}||<1). > > I have in this moment no idea how to calculate > > Int_{0}^{h} ( A* exp(h-s)A ) ds > A is constant w.r.t. to integration. Hence integrate it like normal(think of A as a real number). One gets exp(h*A) - 1. Alternatively use a taylor expansion which will result in the same thing. i.e., exp((h-s)*A) = sum(((h-s)*A)^k/k!) (I assume you mean A*exp((h-s)*A)) |