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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
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