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Volumn 15, Issue 2, 2001, Pages 121-151

Loss and retention of accuracy in affine scaling methods

Author keywords

Accurate computation of small residuals; Affine scaling methods; Convergence properties; Linear 1 problems; Numerical experiments; Rounding errors

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; ITERATIVE METHODS; PROBLEM SOLVING; VECTORS;

EID: 0036457812     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (4)

References (53)
  • 1
    • 0026119751 scopus 로고
    • Limiting behavior of the affine scaling continuous trajectories for linear programming problems
    • Adler, I. and Monteiro, R. D. C. (1991). Limiting behavior of the affine scaling continuous trajectories for linear programming problems, Math. Programming, 50, 29-51.
    • (1991) Math. Programming , vol.50 , pp. 29-51
    • Adler, I.1    Monteiro, R.D.C.2
  • 2
    • 0000110392 scopus 로고
    • An implementation of Karmarkar's algorithm for linear programming
    • Adler, I., Resende, M. G. C., Veiga, G. and Karmarkar, N. (1989). An implementation of Karmarkar's algorithm for linear programming, Math. Programming, 44, 297-335.
    • (1989) Math. Programming , vol.44 , pp. 297-335
    • Adler, I.1    Resende, M.G.C.2    Veiga, G.3    Karmarkar, N.4
  • 3
    • 0022808141 scopus 로고
    • A variation on Karmarkar's algorithm for solving linear programming problems
    • Barnes, E. R. (1986). A variation on Karmarkar's algorithm for solving linear programming problems, Math. Programming, 36, 174-182.
    • (1986) Math. Programming , vol.36 , pp. 174-182
    • Barnes, E.R.1
  • 4
    • 0012096365 scopus 로고
    • Some results concerning convergence of the affine scaling algorithm
    • Barnes, E. R. (1990). Some results concerning convergence of the affine scaling algorithm, Contemporary Math., 114, 131-139.
    • (1990) Contemporary Math. , vol.114 , pp. 131-139
    • Barnes, E.R.1
  • 5
    • 0002671024 scopus 로고
    • Stability analysis of the method of semi-normal equations for least squares problems
    • Bjorck, A. (1987). Stability analysis of the method of semi-normal equations for least squares problems, Linear Algebra and Its Applications, 88/89, 31-48.
    • (1987) Linear Algebra and Its Applications , vol.88-89 , pp. 31-48
    • Bjorck, A.1
  • 10
    • 0012091185 scopus 로고
    • 1 solution of linear equations subject to linear constraints
    • 1 solution of linear equations subject to linear constraints, SIAM J. on Scientific and Statistical Computing, 10, 328-340.
    • (1989) SIAM J. on Scientific and Statistical Computing , vol.10 , pp. 328-340
    • Dax, A.1
  • 11
    • 4244202406 scopus 로고    scopus 로고
    • On theory and practice of affine scaling methods
    • Hydrological Service of Israel
    • Dax, A., On theory and practice of affine scaling methods, Tech. Rep., Hydrological Service of Israel, 1999.
    • (1999) Tech. Rep.
    • Dax, A.1
  • 12
    • 0034379461 scopus 로고    scopus 로고
    • A modified Gram-Schmidt algorithm with iterative orthogonalization and column pivoting
    • Dax, A. (2000). A modified Gram-Schmidt algorithm with iterative orthogonalization and column pivoting, Linear Algebra and Its Applications, 310, 25-42.
    • (2000) Linear Algebra and Its Applications , vol.310 , pp. 25-42
    • Dax, A.1
  • 13
    • 4243449912 scopus 로고    scopus 로고
    • Accurate computation of small projections
    • Hydrological Service of Israel
    • Dax, A., Accurate computation of small projections, Tech. Rep., Hydrological Service of Israel, 2001.
    • (2001) Tech. Rep.
    • Dax, A.1
  • 14
    • 0000754239 scopus 로고
    • Iterative Solution of Problems of Linear and Quadratic Programming
    • Dikin, I. I. (1967). Iterative Solution of Problems of Linear and Quadratic Programming, Soviet Mathematics Doklady, 8, 674-675.
    • (1967) Soviet Mathematics Doklady , vol.8 , pp. 674-675
    • Dikin, I.I.1
  • 16
    • 0024069081 scopus 로고
    • Computer intensive methods in statistical regression
    • Efron, B. (1988). Computer intensive methods in statistical regression, SIAM Review, 30, 421-449.
    • (1988) SIAM Review , vol.30 , pp. 421-449
    • Efron, B.1
  • 17
    • 0000904936 scopus 로고
    • Modifications of the normal equations method that are numerically stable
    • Golub, G. H. and Van Dooren, P. (Eds.), NATO ASI Series, Springer, Verlag, Berlin
    • Foster, L. V., Modifications of the normal equations method that are numerically stable, In: Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, Golub, G. H. and Van Dooren, P. (Eds.), NATO ASI Series, Springer, Verlag, Berlin, 1991, pp. 501-512.
    • (1991) Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms , pp. 501-512
    • Foster, L.V.1
  • 18
    • 0000924593 scopus 로고
    • Numerical methods for solving least squares problems
    • Golub, G. H. (1965). Numerical methods for solving least squares problems, Numerische Mathematik, 7, 206-216.
    • (1965) Numerische Mathematik , vol.7 , pp. 206-216
    • Golub, G.H.1
  • 21
    • 51249181779 scopus 로고
    • A new polynomial-time algorithm for linear programming
    • Karmarkar, N. (1984). A new polynomial-time algorithm for linear programming, Combinatorica, 4, 373-395.
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.1
  • 23
    • 26444614368 scopus 로고
    • 1 Solution of Overdetermined Linear Equations by an Affine Scaling Linear Programming Algorithm, Technical Report
    • Minneapolis, 11 July
    • 1 Solution of Overdetermined Linear Equations by an Affine Scaling Linear Programming Algorithm, Technical Report, Presented at the SIAM National Meeting, Minneapolis, 11 July, 1988.
    • (1988) SIAM National Meeting
    • Leary, R.H.1
  • 24
    • 0031538852 scopus 로고    scopus 로고
    • The affine scaling algorithm fails for γ=0.999
    • Mascarenhas, W. F. (1997). The affine scaling algorithm fails for γ=0.999, SIAM Journal on Optimization, 7, 34-46.
    • (1997) SIAM Journal on Optimization , vol.7 , pp. 34-46
    • Mascarenhas, W.F.1
  • 27
    • 0023591611 scopus 로고
    • Computational Experiments with a Dual Affine Variant of Karmarkar's Method for Linear Programming
    • Monma, C. L. and Morton, A. J. (1987). Computational Experiments with a Dual Affine Variant of Karmarkar's Method for Linear Programming, Operations Research Letters, 6, 261-267.
    • (1987) Operations Research Letters , vol.6 , pp. 261-267
    • Monma, C.L.1    Morton, A.J.2
  • 28
    • 58149362644 scopus 로고
    • Superlinear primal-dual affine scaling algorithms for LCP
    • Monteiro, R. D. C. and Wright, S. (1995). Superlinear primal-dual affine scaling algorithms for LCP, Mathematical Programming, 69, 311-333.
    • (1995) Mathematical Programming , vol.69 , pp. 311-333
    • Monteiro, R.D.C.1    Wright, S.2
  • 29
    • 0030304768 scopus 로고    scopus 로고
    • A superlinear infeasible-interior-point affine scaling algorithm for LCP
    • Monteiro, R. D. C. and Wright, S. (1996). A superlinear infeasible-interior-point affine scaling algorithm for LCP, SIAM Journal on Optimization, 6, 1-18.
    • (1996) SIAM Journal on Optimization , vol.6 , pp. 1-18
    • Monteiro, R.D.C.1    Wright, S.2
  • 30
    • 0032330782 scopus 로고    scopus 로고
    • Global convergence of the affine scaling algorithm for convex quadratic programming
    • Monteiro, R. D. C. and Tsuchiya, T. (1998). Global convergence of the affine scaling algorithm for convex quadratic programming, SIAM Journal on Optimization, 8, 26-58.
    • (1998) SIAM Journal on Optimization , vol.8 , pp. 26-58
    • Monteiro, R.D.C.1    Tsuchiya, T.2
  • 31
    • 0012035936 scopus 로고    scopus 로고
    • Trust region affine scaling algorithms for linearly constrained convex and concave programs
    • Monteiro, R. D. C. and Wang, Y. (1998). Trust region affine scaling algorithms for linearly constrained convex and concave programs, Mathematical Programming, 80, 283-313.
    • (1998) Mathematical Programming , vol.80 , pp. 283-313
    • Monteiro, R.D.C.1    Wang, Y.2
  • 32
    • 0012033076 scopus 로고    scopus 로고
    • A convergence analysis of the projective scaling algorithm based on the long-step homogeneous affine scaling algorithm
    • Muramatsu, M. and Tsuchiya, T. (1996). A convergence analysis of the projective scaling algorithm based on the long-step homogeneous affine scaling algorithm, Mathematical Programming, 72, 291-305.
    • (1996) Mathematical Programming , vol.72 , pp. 291-305
    • Muramatsu, M.1    Tsuchiya, T.2
  • 37
    • 0026171684 scopus 로고
    • The simplex and projective scaling algorithms as iteratively reweighted least squares methods
    • Stone, R. E. and Tovey, C. A. (1991). The simplex and projective scaling algorithms as iteratively reweighted least squares methods, SIAM Review, 33, 220-237.
    • (1991) SIAM Review , vol.33 , pp. 220-237
    • Stone, R.E.1    Tovey, C.A.2
  • 39
    • 0012099573 scopus 로고
    • The affine-scaling direction for linear programming is a limit of projective-scaling directions
    • Todd, M. J. (1991). The affine-scaling direction for linear programming is a limit of projective-scaling directions, Linear Algebra and Its Applications, 152, 93-105.
    • (1991) Linear Algebra and Its Applications , vol.152 , pp. 93-105
    • Todd, M.J.1
  • 40
    • 0022955850 scopus 로고
    • An extension of Karmarkar's algorithm for linear programming using dual variables
    • Todd, M. J. and Burrell, B. P. (1986). An extension of Karmarkar's algorithm for linear programming using dual variables, Algorithmica, 1, 409-424.
    • (1986) Algorithmica , vol.1 , pp. 409-424
    • Todd, M.J.1    Burrell, B.P.2
  • 41
    • 34249836074 scopus 로고
    • On the convergence of the affine-scaling algorithm
    • Tseng, P. and Luo, Z. (1992). On the convergence of the affine-scaling algorithm, Mathematical Programming, 56, 301-319.
    • (1992) Mathematical Programming , vol.56 , pp. 301-319
    • Tseng, P.1    Luo, Z.2
  • 42
    • 34249918986 scopus 로고
    • Global convergence of the affine scaling methods for degenerate linear programming problems
    • Tsuchiya, T. (1991). Global convergence of the affine scaling methods for degenerate linear programming problems, Mathematical Programming Series B, 52, 377-404.
    • (1991) Mathematical Programming Series B , vol.52 , pp. 377-404
    • Tsuchiya, T.1
  • 43
    • 0001329221 scopus 로고
    • Global convergence property of the affine scaling methods for primal degenerate linear programming problems
    • Tsuchiya, T. (1992). Global convergence property of the affine scaling methods for primal degenerate linear programming problems, Mathematics of Operations Research, 17, 527-557.
    • (1992) Mathematics of Operations Research , vol.17 , pp. 527-557
    • Tsuchiya, T.1
  • 44
    • 0012067266 scopus 로고    scopus 로고
    • Affine Scaling Algorithm
    • Terkaly, T. (Ed.), Kluwer Academic Publishers
    • Tsuchiya, T., Affine Scaling Algorithm, In: Interior Point Methods of Mathematical Programming, Terkaly, T. (Ed.), Kluwer Academic Publishers, 1996, pp. 35-82.
    • (1996) Interior Point Methods of Mathematical Programming , pp. 35-82
    • Tsuchiya, T.1
  • 45
    • 0002482037 scopus 로고    scopus 로고
    • Superlinear convergence of the affine scaling algorithm
    • Tsuchiya, T. and Monteiro, R. D. C. (1996). Superlinear convergence of the affine scaling algorithm, Mathematical Programming, 75, 77-110.
    • (1996) Mathematical Programming , vol.75 , pp. 77-110
    • Tsuchiya, T.1    Monteiro, R.D.C.2
  • 46
    • 0001665505 scopus 로고
    • Global convergence of a long-step affine scaling algorithm for degenerate linear programming problems
    • Tsuchiya, T. and Muramatsu, M. (1995). Global convergence of a long-step affine scaling algorithm for degenerate linear programming problems, SIAM Journal on Optimization, 5, 525-551.
    • (1995) SIAM Journal on Optimization , vol.5 , pp. 525-551
    • Tsuchiya, T.1    Muramatsu, M.2
  • 47
    • 0001389460 scopus 로고
    • Computing projections for the Karmarkar algorithm
    • Turner, K. (1991). Computing projections for the Karmarkar algorithm, Linear Algebra and Its Applications, 152, 141-154.
    • (1991) Linear Algebra and Its Applications , vol.152 , pp. 141-154
    • Turner, K.1
  • 48
    • 0024303447 scopus 로고
    • Affine-scaling for linear programs with free variables
    • Vanderbei, R. J. (1989). Affine-scaling for linear programs with free variables, Mathematical Programming, 43, 31-44.
    • (1989) Mathematical Programming , vol.43 , pp. 31-44
    • Vanderbei, R.J.1
  • 50
    • 0000647155 scopus 로고
    • I.I. Dikin's convergence result for the affine-scaling algorithm
    • Vanderbei, R. J. and Lagarias, J. C. (1990). I.I. Dikin's convergence result for the affine-scaling algorithm, Contemporary Mathematics, 114, 109-119.
    • (1990) Contemporary Mathematics , vol.114 , pp. 109-119
    • Vanderbei, R.J.1    Lagarias, J.C.2
  • 51
    • 0022956879 scopus 로고
    • A modification of Karmarkar's linear programming algorithm
    • Vanderbei, R. J., Meketon, M. S. and Freedman, B. A. (1986). A modification of Karmarkar's linear programming algorithm, Algorithmica, 1, 395-407.
    • (1986) Algorithmica , vol.1 , pp. 395-407
    • Vanderbei, R.J.1    Meketon, M.S.2    Freedman, B.A.3
  • 52
    • 85011525994 scopus 로고    scopus 로고
    • Choice of norms for data fitting and function approximation
    • Watson, G. A. (1998). Choice of norms for data fitting and function approximation, Acta Numerica, 7, 337-377.
    • (1998) Acta Numerica , vol.7 , pp. 337-377
    • Watson, G.A.1


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