Global convergence of the basic algorithm on Hessenberg matrices
Author:
Beresford Parlett
Journal:
Math. Comp. 22 (1968), 803817
MSC:
Primary 65.35
MathSciNet review:
0247759
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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Parlett, Convergence of the 𝑄𝑅 algorithm,
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(31 #872)
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B. N. Parlett, (c) "Singular and invariant matrices under the QR algorithm," Math. Comp., v. 20, 1966, pp. 611615. MR 35 #3870.
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Beresford
Parlett, Canonical decomposition of Hessenberg
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H. Wilkinson, Convergence of the 𝐿𝑅,
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 J. G. F. Francis, (a) "The QR transformation: a unitary analogue to the LR transformation. I," Comput. J., v. 4, 1961/62, pp. 265271. MR 23 #B3143. (b) "The QR transformation. II," Comput. J., v. 4, 1961/62, pp. 332345. MR 25 #744. MR 0130111 (23:B3143)
 [2]
 A. S. Householder, The Theory of Matrices in Numerical Analysis, Blaisdell, New York, 1964. MR 30 #5475. MR 0175290 (30:5475)
 [3]
 B. H. Kublanovskaja, "On some algorithms for the solution of the complete problem of proper values," J. Comput. Math. and Math. Phys., v. 1, 1961, pp. 555570.
 [4]
 B. N. Parlett, (a) "Convergence of the QR algorithm," Numer. Math., v. 7, 1965, pp. 187193. MR 31 #872. MR 0176600 (31:872)
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 B. N. Parlett, (b) "The LU and QR transformations," in Mathematical Methods for Digital Computers, Vol. II, Wiley, New York, 1967, Chapter 5. MR 0211638 (35:2516)
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 B. N. Parlett, (c) "Singular and invariant matrices under the QR algorithm," Math. Comp., v. 20, 1966, pp. 611615. MR 35 #3870.
 [7]
 B. N. Parlett, (d) "Canonical decomposition of Hessenberg matrices," Math. Comp., v. 21, 1967, pp. 223227. MR 0228519 (37:4099)
 [8]
 J. H. Wilkinson, "Convergence of the LR, QR, and related algorithms," Comput. J., v. 8, 1965, pp. 7784. MR 32 #590. MR 0183108 (32:590)
 [9]
 J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. MR 32 #1894. MR 0184422 (32:1894)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196802477594
PII:
S 00255718(1968)02477594
Article copyright:
© Copyright 1968
American Mathematical Society
