Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind
Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind
We consider approximations<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace x Subscript n Baseline right-brace"><mml:semantics><mml:mrow><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">\{ {x_n}\}</mml:annotation></mml:semantics></mml:math></inline-formula>obtained by moment discretization to (i) the minimal<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper L 2"><mml:semantics><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:annotation encoding="application/x-tex">{\mathcal {L}_2}</mml:annotation></mml:semantics></mml:math></inline-formula>-norm solution of<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper K x equals y"><mml:semantics><mml:mrow><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi class="MJX-tex-caligraphic" mathvariant="script">K</mml:mi></mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:annotation …