Irr: An algorithm for computing the smallest singular value of large scale matrices

References

• Bai , Z. , Fahey , Mark and Golub , Gene . 1996 . Some large-scale matrix computation problems . J. Comput. Appl Math. , 74 : 71 – 89 .
   Web of Science ®Google Scholar
• Boyd , S. and Balakrishnan , V. 1990 . A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L∞-norm . System Control Letters , 15 : 1 – 7 .
   Web of Science ®Google Scholar
• Cullum , J. , Willoughby , R.A. and Lake , M. 1983 . A Lanczos algorithm for computing singular values and vectors of large matrices . SIAM J. Sci. Stat. Comput. , 4 ( 2 ) : 197 – 215 .
   Web of Science ®Google Scholar
• Demmel , J.W. 1997 . Applied Numerical Linear Algebra , Philadelphia : SIAM press .
   Google Scholar
• Emad , N. 1996 . The Padé-Rayleigh-Ritz method for solving large hermitian eigen-problem . Numer, Algor. , 11 : 159 – 179 .
   Google Scholar
• Fernando , K. and Parlett , B. 1994 . Accurate singular values and differential qd algorithm . Numer. Math. , 67 : 191 – 229 .
   Google Scholar
• Golub , G. and Kahan , W. 1965 . Calculating the singular values and pseudoinverse of a matrix . SIAM J. Numer, Anal. , 2 : 205 – 224 . Series B
   Google Scholar
• Golub , G. 1973 . Some modified matrix eigenvalue problems . SIAM Rev. , 15 : 318 – 334 .
   Web of Science ®Google Scholar
• Golub , G. and Strakös , Z. 1994 . Estimates in quadratic formulas . Numer. Algor. , 8 : 241 – 268 .
   Google Scholar
• Golub , G. and Van Loan , C. 1996 . Matrix Computation , 3rd Edition , Baltimore, MD : John Hopkins University Press .
   Google Scholar
• Gou Hongbin Computing trace of function of matrix to appear
   Google Scholar
• He , C. 1995 . Estimating the distance to uncontrollability: a fast method and a slow one . System Control Letters , 26 ( 4 ) : 275 – 281 .
   Web of Science ®Google Scholar
• He , C. and Watson , G.A. 1999 . An algorithm for computing the distance to instability . SIAM J, Matrix Anal. Appl. , 20 ( 1 ) : 101 – 116 . electronic
   Web of Science ®Google Scholar
• Jiang , E.X. and Zhao , F. 1996 . Numerical Approximation , Fudan University Press . Chinese edition
   Google Scholar
• Jiang , E.X. 1984 . The Symmetric Matrices Computation , Shanghai Science and Technology Press . Chinese edition
   Google Scholar
• Jia , Z. 1997 . Refined iterative algorithms based on Amoldi's process for large unsymmetric eigenproblem . Linear Algebra Appl. , 259 : 1 – 23 .
   Google Scholar
• Paige , C. 1995 . Approximate solutions and eigenvalue bounds from Krylov subspaces . Numer, Linear Algebra Appl. , 2 ( 2 ) : 115 – 133 .
   Web of Science ®Google Scholar
• Parlett , B.N. 1997 . The symmetric eigenvalue problem , Philadelphia : SIAM Press .
   Google Scholar
• Ruhe , A. 1984 . Rational Krylov sequence methods for eigenvalue computation . Linear Algebra Appl. , 58 : 391 – 405 .
   Google Scholar
• Van Der Sluis , A. 1969 . Condition number and equilibration of matrices . Numer, Math. , 14 : 14 – 23 .
   Web of Science ®Google Scholar