Fixed Point Iterations
نویسنده
چکیده
Recall that a vector norm on R is a mapping ‖·‖ : R → R satisfying the following conditions: • ‖x‖ > 0 for x 6= 0. • ‖λx‖ = |λ|‖x‖ for x ∈ R and λ ∈ R. • ‖x+ y‖ ≤ ‖x‖+ ‖y‖ for all x, y ∈ R. Since the space Rn×n of all matrices is also a vector space, it is also possible to consider norms there. In contrast to usual vectors, it is, however, also possible to multiply matrices (that is, the matrices form not only a vector space but also an algebra). One now calls a norm on Rn×n a matrix norm, if the norm behaves well under multiplication of matrices. More precisely, we require the norm to satisfy (in addition) the condition:
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تاریخ انتشار 2014