Spectral Approach to Fractional Power of Operator and Its Matrix Approximation

Key Points

• The research aims to construct fractional powers of operators and establish their matrix approximations using a spectral method.
• Develop a spectral approach that applies to operators not generating a semigroup.
• Calculate the convergence rate of matrix approximations using resolvent estimates.
• Create a practical algorithm for deriving matrix approximations.
• Demonstrated effective convergence rates for matrix approximations.
• Provided a viable algorithm for constructing approximations.
• Supported the theory with illustrative examples.