2. Krylov's methods

2.1 Base construction

All these methods start from a given initial vector x ⁰ having n components. In general, x ⁰ = 0 or a vector with random components is chosen. The initial residual r ⁰ is defined by r ⁰ = b – Ax ⁰ . The Krylov space of order k constructed over A and r ⁰ and denoted ${\mathcal{K}}_k$ (A, r ⁰ ...