| Резюме: | We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-coherent dictionaries in Hilbert spaces. We establish the Lebesgue-type inequalities for OSGA, which show that the OSGA provides an almost optimal approximation on the first <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>1</mn><mo>/</mo><mo stretchy="false">(</mo><mn>18</mn><mspace width="3.33333pt"></mspace><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">s</mi><mo>)</mo><mo>]</mo></mrow></semantics></math></inline-formula> steps. Moreover, we improve the asymptotic constant in the Lebesgue-type inequality of OGA obtained by Livshitz E D.
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