Global convergence of the basic algorithm on Hessenberg matrices

Author:
Beresford Parlett

Journal:
Math. Comp. **22** (1968), 803-817

MSC:
Primary 65.35

DOI:
https://doi.org/10.1090/S0025-5718-1968-0247759-4

MathSciNet review:
0247759

Full-text PDF Free Access

References | Similar Articles | Additional Information

**[1]**J. G. F. Francis, (a) "The*QR*transformation: a unitary analogue to the*LR*transformation. I,"*Comput. J.*, v. 4, 1961/62, pp. 265-271. MR**23**#B3143. (b) "The*QR*transformation. II,"*Comput. J.*, v. 4, 1961/62, pp. 332-345. 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. 555-570.**[4]**B. N. Parlett, (a) "Convergence of the*QR*algorithm,"*Numer. Math.*, v. 7, 1965, pp. 187-193. MR**31**#872. MR**0176600 (31:872)****1.**Correction:*Numer. Math.*, v. 10, 1967, pp. 163-164. MR**35**#5129.**[5]**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)****[6]**B. N. Parlett, (c) "Singular and invariant matrices under the*QR*algorithm,"*Math. Comp.*, v. 20, 1966, pp. 611-615. MR**35**#3870.**[7]**B. N. Parlett, (d) "Canonical decomposition of Hessenberg matrices,"*Math. Comp.*, v. 21, 1967, pp. 223-227. MR**0228519 (37:4099)****[8]**J. H. Wilkinson, "Convergence of the*LR, QR*, and related algorithms,"*Comput. J.*, v. 8, 1965, pp. 77-84. 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:
https://doi.org/10.1090/S0025-5718-1968-0247759-4

Article copyright:
© Copyright 1968
American Mathematical Society