CALCULATING THE SINGULAR VALUES AND PSEUDOINVERSE OF A MATRIX,
Abstract
A numerically stable and fairly fast scheme is described to compute the unitary matrices U and V which transform a given matrix A into a diagonal form sigma = U(*)AV, thus exhibiting A's singular values on sigma's diagonal. The scheme first transforms A to a bidiagonal matrix J, then diagonalizes J. The scheme described here is complicated but does not suffer from the computational difficulties which occasionally afflict some previously known methods. Some applications are mentioned, in particular the use of the pseudo-inverse A(I) = V sigma (I) U(*) to solve least squares problems in a way which dampens spurious oscillation and cancellation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 04, 1964
- Accession Number
- AD0603116
Entities
People
- G. Golub
- W. Kahan
Organizations
- Stanford University