# 代数|MA149-15 Linear Algebra代写 warwick代写

denoted $H_{i}$, i.e., we have
$$H: E \rightarrow E, \quad x=\left(x_{1}, \ldots, x_{m}\right) \rightarrow\left((H x){1}, \ldots,(H x){m}\right),$$
where $x_{i},(H x){i}=H{i}(x) \in E_{i}, i=1, \ldots, m$. The problem at hand is to find a fixed point of $H$. A standard procedure is to approximate such fixed point by variants of the successive approximation procedure

$$x^{k+1}=H\left(x^{k}\right), \quad k=0,1, \ldots .$$
Assume for now that we are working with a (shared memory) parallel computer with $p$ processors $P_{1}, \ldots, P_{p}(p \leqslant m)$ and associate a block of components $J_{j} \subseteq{1, \ldots, m}$ with each processor $P_{j}$. Then a parallel variant of the successive approximation procedure (2) can be implemented as follows (pseudocode for processor $P_{j}$ ):

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