# Consider linear iterations of the form where F R n,n , c R n ,

## Question:

Consider linear iterations of the form

where F ∈ R^{n,n}, c ∈ R^{n}, and the iterations are initialized with x(0) = x_{0}. We assume that the iterations admit a stationary point, i.e., that there exist x? ∈ R^{n} such that

In this exercise, we derive conditions under which x(k) tends to a finite limit for k → ∞. We shall use these results in Exercise 7.7, to set up a linear iterative algorithm for solving systems of linear equations.

1. Show that the following expressions hold for all k = 0, 1, . . .:

2.

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**Related Book For**

## Optimization Models

**ISBN:** 9781107050877

1st Edition

**Authors:** Giuseppe C. Calafiore, Laurent El Ghaoui