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

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References | Similar Articles | Additional Information

**[1]**J. G. F. Francis,*The 𝑄𝑅 transformation: a unitary analogue to the 𝐿𝑅 transformation. I*, Comput. J.**4**(1961/1962), 265–271. MR**0130111**, https://doi.org/10.1093/comjnl/4.3.265**[2]**Alston S. Householder,*The theory of matrices in numerical analysis*, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR**0175290****[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]**Beresford Parlett,*Convergence of the 𝑄𝑅 algorithm*, Numer. Math.**7**(1965), 187–193. MR**0176600**, https://doi.org/10.1007/BF01397692**1.**Correction:*Numer. Math.*, v. 10, 1967, pp. 163-164. MR**35**#5129.**[5]***Mathematical methods for digital computers. Vol. II*, Edited by Anthony Ralston and Herbert S. Wilf, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR**0211638****[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]**Beresford Parlett,*Canonical decomposition of Hessenberg matrices*, Math. Comp.**21**(1967), 223–227. MR**0228519**, https://doi.org/10.1090/S0025-5718-1967-0228519-6**[8]**J. H. Wilkinson,*Convergence of the 𝐿𝑅, 𝑄𝑅, and related algorithms*, Comput. J.**8**(1965), 77–84. MR**0183108**, https://doi.org/10.1093/comjnl/8.3.273**[9]**J. H. Wilkinson,*The algebraic eigenvalue problem*, Clarendon Press, Oxford, 1965. MR**0184422**

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

Article copyright:
© Copyright 1968
American Mathematical Society