The reduction of an arbitrary real square matrix to tridiagonal form using similarity transformations

Author:
C. Donald LaBudde

Journal:
Math. Comp. **17** (1963), 433-437

MSC:
Primary 65.35

DOI:
https://doi.org/10.1090/S0025-5718-1963-0156455-9

MathSciNet review:
0156455

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a new algorithm for reducing an arbitrary real square matrix to tri-diagonal form using real similarity transformations is described. The method is essentially a generalization of a method due to A. S. Householder for accomplishing the same reduction in the case where the matrix is real and symmetric.

**[1]**W. Givens, ``Numerical computation of the characteristic values of a real symmetric matrix,'' Oak Ridge National Laboratory Report ORNL 1574, 1954. MR**0063771 (16:177c)****[2]**W. Givens, ``Computation of plane unitary rotations transforming a general matrix to triangular form,''*J. Soc. Indust. Appl. Math.*, v. 6, 1958, p. 26-50. MR**0092223 (19:1081e)****[3]**A. S. Householder & F. L. Bauer, ``On certain methods for expanding the characteristic polynomial,''*Numer. Math.*, v. 1, 1959, p. 29-37. MR**0100962 (20:7387)****[4]**C. Lanczos, ``An iterative method for the solution of the eigenvalue problem of linear differential and integral operators,''*J. Res. Nat. Bur. Standards*, v. 45, 1950, p. 255-282. MR**0042791 (13:163d)****[5]**H. R. Schwarz, ``Critere de stabilite pour des systemes d'equations a coefficients constants complexes,''*C. R. Acad. Sci. Paris*, v. 242, 1956, p. 325-327. MR**0074609 (17:614f)****[6]**J. H. Wilkinson, ``Stability of the reduction of a matrix to almost triangular and triangular forms by elementary similarity transformations,''*J. Assoc. Comput. Mach.*, v. 6, 1959, p. 336-359. MR**0106542 (21:5273)****[7]**J. H. Wilkinson, ``Householder's method for the solution of the algebraic eigenvalue problem,''*Comput. J.*, v. 3, 1960, p. 23-27. MR**0111131 (22:1995)**

Retrieve articles in *Mathematics of Computation*
with MSC:
65.35

Retrieve articles in all journals with MSC: 65.35

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1963-0156455-9

Article copyright:
© Copyright 1963
American Mathematical Society