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Minimization of norms and logarithmic norms by diagonal similarities. (English) Zbl 0251.65034


MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
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References:

[1] Bauer, F., J. Stoer, andC. Witzgall: Absolute and Monotonic Norms. Num. Math.3, 257–264 (1961). · Zbl 0111.01602
[2] Dahlquist, G.: Stability and Error Bounds in the Numerical Integration of Ordinary Differential Equations. Trans. Royal Institute of Technology, Nr. 130, Stockholm 70, Sweden. · Zbl 0085.33401
[3] Eberlein, P.: On Measures of Non-Normality for Matrices. Am. Math. Monthly72, 995–996 (1965). · Zbl 0142.00301
[4] Henrici, P.: Bounds for Iterates, Inverses, Spectral Variation and Fields of Values of Nonnormal Matrices. Num. Math.4, 24–40 (1962). · Zbl 0102.01502
[5] Householder, A.: The Theory of Matrices in Numerical Analysis. Blaisdell Publ. Co. 1964. · Zbl 0161.12101
[6] Osborne, E.: On Preconditioning of Matrices. J. ACM7, 338–345 (1960). · Zbl 0106.31604
[7] Parlett, B., andC. Reinsch: Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors. Num. Math.13, 293–304 (1969). · Zbl 0184.37703
[8] Ström, T.: On the Use of Majorants for Strict Error Estimation of Numerical Solutions to Ordinary Differential Equations. Techn. Rept. NA 70.10, Dept. of Comp. Science, Royal Institute of Technology, Stockholm 70, Sweden.
[9] Ström, T.: On Logarithmic Norms. Techn. Rept. NA 69.06. Dept. of Comp. Science, Royal Institute of Technology, Stockholm 70, Sweden. · Zbl 0321.15012
[10] Varga, M.: Matrix Iterative Analysis. Prentice Hall. 1962. · Zbl 0133.08602
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