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Singular value decomposition and least squares solutions
  • G. Golub, C. Reinsch
  • Mathematics, Computer Science
  • Milestones in Matrix Computation
  • 1 April 1970
TLDR
Let A be a real m×n matrix with m≧n eigenvalues. Expand
  • 1,845
  • 186
Balancing a matrix for calculation of eigenvalues and eigenvectors
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 andExpand
  • 173
  • 16
Oscillation matrices with spline smoothing
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
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
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  • 3
The QR and QL Algorithms for Symmetric Matrices
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 $$A = QR{\text{ andExpand
  • 59
  • 3
Inversion of Positive Definite Matrices by the Gauss-Jordan Method
Let A be a real n×n matrix and $$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
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 viewExpand
  • 93
RationalQR transformation with Newton shift for symmetric tridiagonal matrices
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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