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Norm bounds for rational matrix functions (1983)

Schmitt, Bernhard

Springer

Numerische Mathematik 42 (1983), S. 379-389

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ISSN: 0945-3245

Keywords: AMS(MOS): 65L20 ; 15A60 ; 65M20 ; CR: 5.17

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary If the field of values of a matrixA is contained in the left complex halfplaneH and a functionf mapsH into the unit disc then ∥f(A)∥2≦1 by a theorem of J.v. Neumann. We prove a theorem of this type, only the field of values ofA is used for functions which are absolutely bounded by one in only part ofH. An extension can be used to show norm-stability of single step methods for stiff differential equations. The results are applicable among others to several subdiagonal Padé approximations which are notA-stable.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01389581

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