• Publications
• Influence
Singular value decomposition and least squares solutions
• Mathematics, Computer Science
• Milestones in Matrix Computation
• 1 April 1970
Let A be a real m×n matrix with m≧n eigenvalues. Expand
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• 186
Balancing a matrix for calculation of eigenvalues and eigenvectors
• Mathematics
• 1 August 1969
This algorithm is based on the work of Osborne . He pointed out that existing eigenvalue programs usually produce results with errors at least of order e‖A‖ E , where is the machine precision andExpand
• 173
• 16
Oscillation matrices with spline smoothing
• 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 oscillationExpand
• 92
• 8
Handbook for Automatic Computation. Vol II, Linear Algebra
• 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 matrixExpand
• 254
• 3
The QR and QL Algorithms for Symmetric Matrices
• Mathematics
• 1971
The QR algorithm as developed by Francis  and Kublanovskaya  is conceptually related to the LR algorithm of Rutishauser . It is based on the observation that if $$A = QR{\text{ andExpand • 59 • 3 Inversion of Positive Definite Matrices by the Gauss-Jordan Method • Physics • 1971 Let A be a real n×n matrix and$$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 remainingExpand
• 18
• 1
Householder's tridiagonalization of a symmetric matrix
• Mathematics
• 1 March 1968
In an early paper in this series  Householder’s algorithm for the tridiagonalization of a real symmetric matrix was discussed. In the light of experience gained since its publication and in viewExpand
• 93
RationalQR transformation with Newton shift for symmetric tridiagonal matrices
• 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. IfExpand
• 26
Two Extensions of the Sard--Schoenberg Theory of Best Approximation
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 $x_1 , \cdots ,x_n \in [a,b]$. TheExpand
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