Vector space Krylov subspace

The power method uses only the last vector in the recursive sequence in Eq. [21], discarding all information provided by preceding vectors. It is not difficult to imagine that significantly more information may be extracted from the space spanned by these vectors, which is often called the Krylov subspace- 0,14... 

An alternative solution to this problem is provided by fast Krylov-space algorithms. " These techniques construct a small subspace of orthogonal vectors which contains a good approximation to the true eigenvector. This Krylov subspace 5p, . ..,... 

Definition 16 The finite dimensional subspace Ki of the Euclidean space E, spanned by the vectors c. Be,., ..B c, is called a Krylov space ... 

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