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Publications Influence

Singular value decomposition and least squares solutions

- G. Golub, C. Reinsch
- Mathematics, Computer Science
- Milestones in Matrix Computation
- 1 April 1970

TLDR

1,845 186

Balancing a matrix for calculation of eigenvalues and eigenvectors

- B. Parlett, C. Reinsch
- Mathematics
- 1 August 1969

This algorithm is based on the work of Osborne [1]. He pointed out that existing eigenvalue programs usually produce results with errors at least of order e‖A‖ E , where is the machine precision and… Expand

173 16

Oscillation matrices with spline smoothing

- A. Demmler, C. Reinsch
- Mathematics
- 1 October 1975

SummarySpline smoothing can be reduced to the minimization of a certain quadratic form with positive semidefinite matrix. For polynomial splines this matrix is closely related to an oscillation… Expand

92 8

Handbook for Automatic Computation. Vol II, Linear Algebra

- J. H. Wilkinson, C. Reinsch
- Mathematics
- 1 July 1973

Haida gwaii tourism guide · Handbook of raman spectroscopy free download Handbook for automatic computation vol 2 linear algebra pdf · How much does. the Jordan form, Kronecker's form for matrix… Expand

254 3

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

Inversion of Positive Definite Matrices by the Gauss-Jordan Method

- F. L. Bauer, C. Reinsch
- Physics
- 1971

Let A be a real n×n matrix and
$$y = Ax $$
(1)
the induced mapping R n → R n . If a 1,1 ≠ 0, then one can solve the first of these equations for x 1 and insert the result into the remaining… Expand

18 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

TheQR andQL algorithms for symmetric matrices

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

69

RationalQR transformation with Newton shift for symmetric tridiagonal matrices

- C. Reinsch, F. L. Bauer
- Mathematics
- 1 March 1968

If some of the smallest or some of the largest eigenvalues of a symmetric (tridiagonal) matrix are wanted, it suggests itself to use monotonic Newton corput rections in combination with Q R steps. If… Expand

26

Two Extensions of the Sard--Schoenberg Theory of Best Approximation

- C. Reinsch
- Mathematics
- 1 March 1974

A linear functional $J(f)$ defined on $C^{m - 1} [a,b]$ can be approximated by appropriate linear combinations of function values $f(x_i )$ at discrete points $x_1 , \cdots ,x_n \in [a,b]$. The… Expand

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