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References
Bargmann, V., D. Montgomery andJ. von Neumann: Solution of linear systems of high order. Report prepared under contract NORD 9596 with the Bureau of Ordnance, Navy Department, Institute for Advanced Study, 1946.
Bauer, F. L.: On the definition of condition numbers and their relation to closed methods for solving linear systems. Proceedings of the International Conference on Information Processing, Unesco, Paris 1960, pp. 109–110.
—, andA. S. Householder: Moments and characteristic roots. Numerische Math.2, 42–53 (1960).
—, andC. T. Fike: Norms and exclusion theorems. Numerische Math.2, 137–141 (1960).
Farnell, A. B.: Limits for the field of values of a matrix. Amer. Math. Monthly52, 488–493 (1945).
Forsythe, G. E.: Singularity and near singularity in numerical analysis. Amer. Math. Monthly65, 229–240 (1958).
Gautschi, We: The asymptotic behavior of powers of matrices. Duke Math. J.20, 127–140 (1953).
—: The asymptotic behavior of powers of matrices. II. Duke Math. J.20, 375–379 (1953).
Givens, W.: Fields of values of a matrix. Proc. Amer. Math. Soc.3, 206–209 (1952).
Hausdorff, E.: Der Wertevorrat einer Bilinearform. Math. Z.3, 314–316 (1919).
Hoffmann, A. J., andH. W. Wielandt: The variation of the spectrum of a normal matrix. Duke Math. J.20, 37–39 (1953).
Householder, A. S.: The approximate solution of matrix problems. J. Assoc. Comput. Mach.5, 204–243 (1958).
Kato, T.: Estimation of iterated matrices, with application to the von Neumann condition. Numerische Math.2, 22–29 (1960).
Kippenhahn, R.: Über den Wertevorrat einer Matrix. Math. Nachrichten6, 193–228 (1951).
Lax, P. D., andR. D. Richtmyer: Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math.9, 267–293 (1956).
McRae, V. V.: On the unitary similarity of matrices. Ph. D. Dissertation, Catholic University of America, 1955.
Mirsky, L.: An introduction to linear algebra. Oxford: Oxford University Press 1955.
Morrison, D. D.: Errors in the solution of eigenvalue problems by finite difference methods. Ph. D. Dissertation, University of California, Los Angeles, 1961.
Murnaghan, F. D.: On the field of values of a square matrix. Proc. Nat. Acad. Sci. U.S.A.18, 246–248 (1932).
Ostrowski, A.: Über Normen von Matrizen. Math. Z.63, 2–18 (1955).
—: Über die Stetigkeit von charakteristischen Wurzeln in Abhängigkeit von den Matrizenelementen. Jahresber. Dtsch. Math. Verein.60, Abt. 1, 40–42 (1957).
Ostrowski, A.: On the continuity of characteristic roots in their dependence on the matrix elements (translation of [21]). Translated from the German and annotated byG. E. Bump. Technical Report No. 2, Project 225(37), Applied Mathematics and Statistics Laboratories, Stanford University, 1959.
—: Solution of equations and systems of equations. New York and London: Academic Press 1960.
Parker, W. V.: Characteristic roots and fields of values of a matrix. Bull. Amer. Math. Soc.57, 103–108 (1951).
Stone, B. J.: Best possible ratios of certain matrix norms. Numer. Math., to appear.
Toeplitz, O.: Das algebraische Analogon zu einem Satz vonFejér. Math. Z.,2, 187–197 (1918).
White, P. A.: The computation of eigenvalues and eigenvectors of a matrix. J. Soc. Indust. Appl. Math.6, 393–437 (1958).
Wielandt, H.: Inclusion theorems for eigenvalues. Nat. Bur. Standards Appl. Math. Ser.29, 75–78 (1951).
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Henrici, P. Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices. Numer. Math. 4, 24–40 (1962). https://doi.org/10.1007/BF01386294
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DOI: https://doi.org/10.1007/BF01386294