Geodesic
Operator interpolation is one of universal methods of approximation theory
Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 17-31

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The article is mainly a survey. It outlines general approaches to constructing interpolation operator polynomials in abstract linear and functional spaces and provides a number of specific formulas for operator interpolation. Interpolation of functions of matrix variables is also considered. 
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M. V. Ignatenko; L. A. Yanovich. Operator interpolation is one of universal methods of approximation theory. Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 17-31. http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a2/