Submitted:
06 January 2026
Posted:
08 January 2026
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Abstract
This article is devoted to constructing of fractional powers of operators and their matrix approximations. A key feature of this study is the use of a spectral approach that remains applicable even when the base operator does not generate a semigroup.
Our main results include the convergence rate of matrix approximation, derived from resolvent estimates, and a practical algorithm for constructing matrix approximations. The theory is supported by examples.
Keywords:
fractional integrals
; resolvent
; rate of convergence
; powers of matrix operator
; matrix approximation
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