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  • Linear Programming  (1)
  • Quasi-interpolation formulae  (1)
  • 1
    Electronic Resource
    Electronic Resource
    A nonlinear equation for linear programming (1986)
    Springer
    Mathematical programming 34 (1986), S. 235-238 
    Details
    ISSN: 1436-4646
    Keywords: Linear Programming ; Characterization of Optimality ; Dual Program
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a characterization of the ‘normal’ optimal solution of the linear program given in canonical form max{c tx: Ax = b, x ≥ 0}. (P) We show thatx * is the optimal solution of (P), of minimal norm, if and only if there exists anR 〉 0 such that, for eachr ≥ R, we havex * = (rc − Atλr)+. Thus, we can findx * by solving the following equation forλ r A(rc − Atλr)+ = b. Moreover,(1/r)λ r then ‘converges’ to a solution of the dual program.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580588
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Quasi-interpolants from spline interpolation operators (1990)
    Springer
    Constructive approximation 6 (1990), S. 97-110 
    Details
    ISSN: 1432-0940
    Keywords: Toeplitz matrix ; Quasi-interpolation formulae ; Poisson summation formula ; Primary 41A15 ; Secondary 41A05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For bi-infinite Toeplitz matrices, it is easy to see that thekth partial sum of the Neumann series reproduces polynomials of orderk There is no guarantee, however, that the spectral radius is less than 1. A principal result of this paper is to show that for the spline interpolation Toeplitz case the spectral radius is less than 1 whenA is invertible and the main diagonal is the central diagonal. This is not true for all totally positive Toeplitz matrices as shown by an example in Section 2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01891410
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    Paper (German National Licenses)
    Fulltext
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