Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 335 / 3 / ii

Solution

A^{*} A x = A^{*} y .

x_{n + 1} = x_{n} + γ A^{*} (y - A x_{n}) = (I - γ A^{*} A) x_{n} + γ A^{*} y .

A sufficient step-size condition is

0 < γ < \frac{2}{∥ A ∥ ^{2}} .

y \in D (A^{†})

and

x_{0} \in (ker A)^{⊥}

, then

x_{n} ⟶ A^{†} y .

For an arbitrary initial iterate, its null-space component is unchanged and the limit is

A^{†} y + P_{k e r A} x_{0} .

There are no discussions about this article yet.

There are currently no matching articles.