Re: [eigen] Generalized selfadjoint eigenvalues |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Generalized selfadjoint eigenvalues*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Thu, 10 Jun 2010 17:00:56 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:mime-version:received:in-reply-to :references:from:date:message-id:subject:to:content-type; bh=lIjGm7eoufDkkUfB5gcY70xXJH4/O9wqZLyjTbOcT78=; b=O5zrpuOFNffipJe5iuC9ncPSMo5/U7lYY5E9Akvis5HwD7VLW8y4syeTKwP+7hTJU1 K7r8p9RizMai8UNhVYFevUKOQfdBOQ6bxLFU5OpPXfDpMd6AEQ0SXf50SLPdnOs5DD4y 35x9gdr/3lNlqIlzIEO1MtEsVFlFCb6cjMphQ=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-type; b=GpmKZjwEb1FN1XoN5mwAZ9qUsMTk1eeLNDW9F5tmm3DBjWWoZpj9lLSUVuc4DgrDha wBsVXKdYhqzT1fiNYJPX9qVQyxw/HoyxlBzdKkvkCDJ3OEzzr1tkG3Q/udToL/y/EmqJ Hd7y0zD5WdU8jMRJGZ64j1efZ2Zn5dOc3ec/g=

On Thu, Jun 10, 2010 at 1:56 PM, Helmut Jarausch <jarausch@xxxxxxxxxxxxxxxxxxx> wrote: > On 10 Jun, Jitse Niesen wrote: >> On Thu, 10 Jun 2010, Gael Guennebaud wrote: >> >>> I have some API concerns about the generalized selfadjoint eigenvalues. >> >> Oops, I postponed that part of the Eigenvalues module because I don't know >> much about generalized eigenvalue problems and promptly forgot about it. >> >>> [...] 1 - we might also want to offer the possibility to solve the two >>> other variants: >>> BAx = lambda x >>> ABx = lambda x >> >> Stupid question: why not compute the (non-generalized) eigenvalues of the >> product BA or AB? If the normalization x^* B x = 1 is important, that can >> easily be fixed afterwards? > > Just a comment. > If one transforms the generalized eigenvalue problem A*x= lambda*B*x > to a standard one :: B_inverse * A * x = lambda*x > > one has to invert B and to mupliply two matrices. > This costly and introduce unnecessary rounding errors! Well the main problem is that the product of two selfadjoint matrices is not selfadjoint anymore, and so you would have to use a much more expensive eigenvalue routine. gael > -- > Helmut Jarausch > > Lehrstuhl fuer Numerische Mathematik > RWTH - Aachen University > D 52056 Aachen, Germany > > >

**References**:**[eigen] Generalized selfadjoint eigenvalues***From:*Gael Guennebaud

**Re: [eigen] Generalized selfadjoint eigenvalues***From:*Jitse Niesen

**Re: [eigen] Generalized selfadjoint eigenvalues***From:*Helmut Jarausch

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