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Laguerre's method applied to the matrix eigenvalue problem

Author: Beresford Parlett
Journal: Math. Comp. 18 (1964), 464-485
MSC: Primary 65.40
MathSciNet review: 0165668
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  • [1] Report on the algorithmic language ALGOL 60, Acta Polytech. Scandinav. No. 284 (1960), 40. MR 0130074,
  • [2] E. Durand, Solutions numériques des équations algébriques. Tome I: Équations du type 𝐹(𝑥)=0; racines d’un polynôme, Masson et Cle, Editeurs, Paris, 1960 (French). MR 0121987
  • [3] P. J. Eberlein, A Jacobi-like method for the automatic computation of eigenvalues and eigenvectors of an arbitrary matrix, J. Soc. Indust. Appl. Math. 10 (1962), 74–88. MR 0139264
  • [4] Werner L. Frank, Computing eigenvalues of complex matrices by determinant evaluation and by methods of Danilewski and Wielandt, J. Soc. Indust. Appl. Math. 6 (1958), 378–392. MR 0103586
  • [5] E. N. Laguerre, Oeuvres de Laguerre, Gauthier-Villars, Paris, Vol. 1, p. 87-103.
  • [6] Hans J. Maehly, Zur iterativen Auflösung algebraischer Gleichungen, Z. Angew. Math. Physik 5 (1954), 260–263 (German). MR 0063146
  • [7] B. N. Parlett, Applications of Laguerre's Method to the Matrix Eigenvalue Problem, Tech. Report No. 21, Stanford Univ., Applied Math. and Stat. Labs., Contract Nonr 225(37), 1962.
  • [8] J. B. Rosser, C. Lanczos, M. R. Hestenes, and W. Karush, Separation of close eigenvalues of a real symmetric matrix, J. Research Nat. Bur. Standards 47 (1951), 291–297. MR 0048914
  • [9] Paul A. White, The computation of eigenvalues and eigenvectors of a matrix, J. Soc. Indust. Appl. Math. 6 (1958), 393–437. MR 0100350
  • [10] J. H. Wilkinson, Determination of Characteristic Values and Characteristic Vectors, Application of Advanced Numer. Anal. to Digital Computers, Summer Session, 1958, Univ. of Michigan, Ann Arbor, Mich., p. 101-154.
  • [11] J. H. Wilkinson, Notes on Practical Methods of Solving Linear Systems and Calculating the Eigensystems of Matrices, National Physical Laboratory, Teddington, England, 1959.
  • [12] J. H. Wilkinson, Advanced Numerical Analysis, Summer Session, 1960, Univ. of Michigan, Ann Arbor, Mich.
  • [13] J. H. Wilkinson, Error analysis of floating-point computation, Numer. Math. 2 (1960), 319–340. MR 0116477,
  • [14] J. H. Wilkinson, Stability of the reduction of a matrix to almost triangular and triangular forms by elementary similarity transformations, J. Assoc. Comput. Mach. 6 (1959), 336–359. MR 0106542,
  • [15] J. H. Wilkinson, The Numerical Eigenvalue Problem, Oxford Univ. Press, in preparation.

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Article copyright: © Copyright 1964 American Mathematical Society

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