Glas List: Re: [glas] norms and inner products for vectors of matrices

From: Wolfgang Bangerth (bangerth_at_[hidden])
Date: 2006-01-08 12:40:05

> Talking about vectors of matrices, we need to define algorithms for those:
> let v be a vector of matrices, so v[i] is a matrix,
>
> Then norm_1 could be:
> sum_i norm_1( v[i] )
>
> Norm_inf:
> max_i norm_inf(v[i])
>
> and similarly for other norm functions.
>
> For the inner product, trans(v)*w is then
> sum_i trans(v[i]) * w[i]
>
> Is this ok?

Certainly, at least for the norm. For the inner product, should it be
  trans(v[i]) * w[i]
or
  v[i] * w[i]
I guess the former makes sense if one thinks of vectors that have a block
structure (in your diction, each block would be a n times 1 matrix).

Best
  W.

-------------------------------------------------------------------------
Wolfgang Bangerth                email:            bangerth_at_[hidden]
                                 www: http://www.math.tamu.edu/~bangerth/