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Publications Influence

Symmetric decomposition of a positive definite matrix

- R. Martin, G. Peters, J. H. Wilkinson
- Mathematics
- 1 October 1965

111 3

TheQ R algorithm for real hessenberg matrices

- R. Martin, G. Peters, J. H. Wilkinson
- Mathematics
- 1 February 1970

The QR algorithm of Francis [1] and Kublanovskaya [4] with shifts of origin is described by the relations
$$ \matrix{ {{Q_s}({A_s} - {k_s}I) = {R_s},} & {{A_{s + 1}} = {R_s}Q_s^T + {k_s}I,} &… Expand

74 3- PDF

The QR and QL Algorithms for Symmetric Matrices

- H. Bowdler, R. Martin, C. Reinsch, J. H. Wilkinson
- Mathematics
- 1971

The QR algorithm as developed by Francis [2] and Kublanovskaya [4] is conceptually related to the LR algorithm of Rutishauser [7]. It is based on the observation that if
$$A = QR{\text{ and… Expand

59 3

Reduction of the symmetric eigenproblemAx=λBx and related problems to standard form

- R. Martin, J. H. Wilkinson
- Mathematics
- 1 February 1968

In many fields of work the solution of the eigenproblems Ax = λBx and A B x = λ x (or related problems) is required, where A and B are symmetric and B is positive definite. Each of these problems can… Expand

83 2

Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection

- W. Barth, R. Martin, J. H. Wilkinson
- 1967

29 2

Symmetric decomposition of positive definite band matrices

- R. Martin, J. H. Wilkinson
- Mathematics
- 1 October 1965

The method is based on the following theorem. If A is a positive definite matrix of band form such that
$${a_{ij}} = 0{\rm{ (|}}i - j| >m{\rm{)}}$$
(1)
then there exists a real non-singular… Expand

70 1

Iterative Refinement of the Solution of a Positive Definite System of Equations

- R. Martin, G. Peters, J. H. Wilkinson
- Mathematics
- 1 May 1966

In an earlier paper in this series [1] the solution of a system of equations Ax=b with a positive definite matrix of coefficients was described; this was based on the Cholesky factorization of A. If… Expand

38 1

The implicit QL algorithm

- A. Dubrulle, R. Martin, J. H. Wilkinson
- Mathematics
- 1971

In [1] an algorithm was described for carrying out the QL algorithm for a real symmetric matrix using shifts of origin. This algorithm is described by the relations
$$\matrix{ {{Q_s}({A_s} -… Expand

38 1

Householder's tridiagonalization of a symmetric matrix

- R. Martin, C. Reinsch, J. H. Wilkinson
- Mathematics
- 1 March 1968

In an early paper in this series [4] Householder’s algorithm for the tridiagonalization of a real symmetric matrix was discussed. In the light of experience gained since its publication and in view… Expand

93

Solution of real and complex systems of linear equations

- H. Bowdler, R. Martin, G. Peters, J. H. Wilkinson
- Mathematics
- 1 May 1966

If A is a non-singular matrix then, in general, it can be factorized in the form A = LU, where L is lower-triangular and U is upper-triangular. The factorization, when it exists, is unique to within… Expand

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