The mathematical theory of Krylov subspace methods with a focus on
solving systems of linear algebraic equations is given a detailed
treatment in this principles-based book. Starting from the idea of
projections, Krylov subspace methods are characterised by their
orthogonality and minimisation properties. Projections onto highly
nonlinear Krylov subspaces can be linked with the underlying
problem of moments, and therefore Krylov subspace methods can be
viewed as matching moments model
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