## Glas :## Re: [glas] dotc and dotu in glas |

**From:** Karl Meerbergen (*Karl.Meerbergen_at_[hidden]*)

**Date:** 2006-05-04 02:49:42

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Hello,

Where could a vectorspace concept be used?

Iterative methods, time integration.

When I look at my own implementations for those, I think the following

list is pretty complete for linear system solvers with a single

right-hand side. (Although, for efficient implementation of gmres and

bicgstab(ell), we also need matrices for storing basis vectors and

matrix vector operations)

Operations:

Let v, and w be vectors, s a scalar.

v += w

v -= w

v += s*w

v -= s*w

v *= s

v /= s

s * v returning a vector expression

v / s returning a vector expression

v = vector expression

The following operations can be written as a combination of the previous

ones.

v - w returning a vector expression

v + w returning a vector expression

-v returning a vector expression

Creation of new containers (vectors in the vector space) for auxiliary

results.

inner_product(x,y) (can be implemented via dotc() or dotu() or dot() or

x^HERM * y or whathever syntax we decide to use when a Euclidean

vectorspace is used), where x and y belong to the same vectorspace.

bilinear_form(x,y) for x and y in a different vectorspace.

norm(x) (can be implemented using norm_2(x) when a Euclidean vectorspace

is used)

Can vectors x and y of different types below to the same vectorspace?

What about subspaces, etc.?

Karl

**Next message:**Toon Knapen: "Re: [glas] dotc and dotu in glas"**Previous message:**Karl Meerbergen: "Re: [glas] dotc and dotu in glas"**In reply to:**Karl Meerbergen: "Re: [glas] dotc and dotu in glas"**Next in thread:**Toon Knapen: "Re: [glas] dotc and dotu in glas"