메뉴 건너뛰기




Volumn 66, Issue 220, 1997, Pages 1487-1508

Equivalent formulae for the supremum and stability of weighted pseudoinverses

Author keywords

Stability; Supremum; Weighted pseudoinverse

Indexed keywords


EID: 0031488886     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00899-5     Document Type: Article
Times cited : (6)

References (24)
  • 2
    • 38249016652 scopus 로고
    • A geometric property of the least squares solution of linear Equations
    • MR 91h:15004
    • A. Ben-Tal and M. Teboulle, A geometric property of the least squares solution of linear Equations, Linear Algebra Appl. 139 (1990), 165-170. MR 91h:15004
    • (1990) Linear Algebra Appl. , vol.139 , pp. 165-170
    • Ben-Tal, A.1    Teboulle, M.2
  • 3
    • 0001935197 scopus 로고
    • On the speed of an iterative process
    • I.I. Dikin, On the speed of an iterative process, Upravlyaemye Sistemi 12 (1974), 54-60.
    • (1974) Upravlyaemye Sistemi , vol.12 , pp. 54-60
    • Dikin, I.I.1
  • 4
    • 0030490110 scopus 로고    scopus 로고
    • On linear least-squares problems with diagonally dominant weight matrices
    • CMP 97:01
    • A. Forsgren, On linear least-squares problems with diagonally dominant weight matrices, SIAM J. Matrix Anal. Appl. 17 (1996), 763-788. CMP 97:01
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 763-788
    • Forsgren, A.1
  • 5
    • 0030531116 scopus 로고    scopus 로고
    • Stability of symmetric ill-conditioned systems arising in interior methods for constrained optimization
    • MR 96m:90084
    • A. Forsgren, P.E. Gill and J.R. Shinnerl, Stability of symmetric ill-conditioned systems arising in interior methods for constrained optimization, SIAM J. Matrix Anal. Appl. 17 (1996), 187-211. MR 96m:90084
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 187-211
    • Forsgren, A.1    Gill, P.E.2    Shinnerl, J.R.3
  • 8
    • 0026876871 scopus 로고
    • Path-following methods for linear programming
    • MR 93j:90050
    • C.C. Gonzaga, Path-following methods for linear programming, SIAM Review 34 (1992), 167-224. MR 93j:90050
    • (1992) SIAM Review , vol.34 , pp. 167-224
    • Gonzaga, C.C.1
  • 9
    • 21144476232 scopus 로고
    • Modifying the QR decomposition to constrained and weighted linear least squares
    • MR 93e:65066
    • M. Gullikson and P.-Å. Wedin, Modifying the QR decomposition to constrained and weighted linear least squares, SIAM J. Matrix Anal. Appl. 13 (1992), 1298-1313. MR 93e:65066
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 1298-1313
    • Gullikson, M.1    Wedin, P.-Å.2
  • 10
    • 21144466811 scopus 로고
    • The geometry of the set of scaled projections
    • MR 94g:15002
    • M. Hanke and M. Neumann, The geometry of the set of scaled projections, Linear Algebra Appl. 190 (1993), 137-148. MR 94g:15002
    • (1993) Linear Algebra Appl. , vol.190 , pp. 137-148
    • Hanke, M.1    Neumann, M.2
  • 11
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, UK, MR 87e:15001
    • R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985. MR 87e:15001
    • (1985) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 12
    • 0001500190 scopus 로고
    • On bounds for scaled projections and pseudoinverses
    • MR 91f:15056
    • D. P. O'Leary, On bounds for scaled projections and pseudoinverses, Linear Algebra, Appl. 132 (1990), 115-117. MR 91f:15056
    • (1990) Linear Algebra, Appl. , vol.132 , pp. 115-117
    • O'Leary, D.P.1
  • 13
    • 0010992667 scopus 로고
    • The geometry of basic, approximate, and minimum-norm solution of linear equations
    • MR 96e:15003
    • J. Miao and A. Ben-Israel, The geometry of basic, approximate, and minimum-norm solution of linear equations, Linear Algebra Appl. 216 (1995), 25-41. MR 96e:15003
    • (1995) Linear Algebra Appl. , vol.216 , pp. 25-41
    • Miao, J.1    Ben-Israel, A.2
  • 14
    • 0001129014 scopus 로고
    • Towards a generalized singular value decomposition
    • MR 83c:65082
    • C.C. Paige and M.A. Saunders, Towards a generalized singular value decomposition, SIAM J. Numer. Anal. 18 (1981), 398-405. MR 83c:65082
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 398-405
    • Paige, C.C.1    Saunders, M.A.2
  • 15
    • 0000685126 scopus 로고
    • On scaled projections and pseudoinverses
    • MR 90d:15005
    • G.W. Stewart, On scaled projections and pseudoinverses, Linear Algebra Appl. 112 (1989), 189-193. MR 90d:15005
    • (1989) Linear Algebra Appl. , vol.112 , pp. 189-193
    • Stewart, G.W.1
  • 17
    • 0000647155 scopus 로고
    • Dikin's convergence result for the affine-scaling algorithm
    • MR 92d:90046
    • R.J. Vanderbei and J.C. Lagarias, Dikin's convergence result for the affine-scaling algorithm, Contemporary Mathematics 114 (1990), 109-119. MR 92d:90046
    • (1990) Contemporary Mathematics , vol.114 , pp. 109-119
    • Vanderbei, R.J.1    Lagarias, J.C.2
  • 18
    • 21844522941 scopus 로고
    • Stable numerical algorithms for equilibrium system
    • MR 95m:65080
    • S.A. Vavasis, Stable numerical algorithms for equilibrium system, SIAM J. Matrix Anal. Appl. 15 (1994), 1108-1131. MR 95m:65080
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 1108-1131
    • Vavasis, S.A.1
  • 19
    • 0040235745 scopus 로고
    • Algebraic properties of the rank- deficient equality constrained and weighted least squares problems
    • MR 92j:65059
    • M. Wei, Algebraic properties of the rank- deficient equality constrained and weighted least squares problems, Linear Algebra Appl. 161 (1992), 27-43. MR 92j:65059
    • (1992) Linear Algebra Appl. , vol.161 , pp. 27-43
    • Wei, M.1
  • 20
    • 0026938285 scopus 로고
    • Perturbation theory for the rank- deficient equality constrained least squares problem
    • MR 93i:65046
    • M. Wei, Perturbation theory for the rank- deficient equality constrained least squares problem, SIAM J. Numer. Anal. 29 (1992), 1462-1481. MR 93i:65046
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1462-1481
    • Wei, M.1
  • 21
    • 21844514937 scopus 로고
    • Upper bound and stability of scaled pseudoinverses
    • MR 96k:65031
    • M. Wei, Upper bound and stability of scaled pseudoinverses, Numer. Math. 72 (1995), 285-293. MR 96k:65031
    • (1995) Numer. Math. , vol.72 , pp. 285-293
    • Wei, M.1
  • 22
    • 84971922797 scopus 로고
    • Interior methods for constrained optimization
    • A. Iserles, edit., Cambridge University Press, Cambridge, UK, MR 93d:90037
    • M.H. Wright, Interior methods for constrained optimization, In A. Iserles, edit., Acta Numerica, pp.341-407, Cambridge University Press, Cambridge, UK, 1992. MR 93d:90037
    • (1992) Acta Numerica , pp. 341-407
    • Wright, M.H.1
  • 23
    • 0039014262 scopus 로고
    • Stability of linear equations solvers in interior-point methods
    • MR 96f:65055
    • S. Wright, Stability of linear equations solvers in interior-point methods, SIAM J. Matrix Anal. Appl. 16 (1995), 1287-1307. MR 96f:65055
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 1287-1307
    • Wright, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.