Re: [eigen] Matrix exponential |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Matrix exponential*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Wed, 6 May 2009 14:25:52 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=iug4Gccb+udCNKHzUC9LGVOJ2ROGf9TLX5rbwqD+bH0=; b=tX8fq3qc1gNmAEypZ8T546HXtsb7HXjFROwy0oDmc6MMxrT0T6mc3Wt+DVWOReadIW 1bNMg33vDAPbcQ1yCk7hYgPuKVwnh7vhJc+N6Zq0KFVbzHBpD8jIJBxP0XDdEkG3Ewbg NMGVdmRpWgc1kOG773LTCmKH4UswW05OvqF+U=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=PVNoB8bUIJ2Xy4Ly1F0t73k4SbAXQJSZmp48bP1ykBUNUsybBVEfQZfsbvRoijS8qI JQK47K1U/bTIbqYOglOb1UO9ar4RTlwdnmKcdUtudj3H+JASTT7b8ZMOhexB2WAYeDK/ tEdQd98+4VgHSU90UB2CPrOANpMQXtHNtahak=

Yes, I agree it's useful especially since i realized that the other approach of exponentiating eigenvalues.... only applies to diagonalizable matrices! The complexity of the present approach is said to be roughly 20n^3 which is huge, though, and in practice, the most common case is exponentiating a skew-adjoint matrix (think exp(itH) where H is a hamiltonian, think Stone's theorem...), whose diagonalization boils down to diagonalization of a selfadjoint matrix. So it'd be very important to make sure the selfadjointeigensolver is robust enough that it can always safely be used without convergence issues! Benoit 2009/5/6, Thomas Capricelli <orzel@xxxxxxxxxxxxxxx>: > > > Great, I will make use of those methods, thank you ! > > Thomas > > On Tuesday 05 May 2009 22:47:52 Benoit Jacob wrote: >> Thanks for the patch, it looks good, including the appropriate use of >> .lazy() ;) >> It's committed in r964042. > > -- > Thomas Capricelli <orzel@xxxxxxxxxxxxxxx> > http://www.freehackers.org/thomas > > >

**Follow-Ups**:**Re: [eigen] Matrix exponential***From:*Jitse Niesen

**References**:**Re: [eigen] Matrix exponential***From:*Jitse Niesen

**Re: [eigen] Matrix exponential***From:*Benoit Jacob

**Re: [eigen] Matrix exponential***From:*Thomas Capricelli

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