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2 results

  • A Generalization of Takane's Algorithm for Dedicom

  • Henk A. L. Kiers, Jos M. F. ten Berge, Yoshio Takane, Jan de Leeuw
  • Journal:
    Psychometrika / Volume 55 / Issue 1 / March 1990
    Published online by Cambridge University Press:
    01 January 2025, pp. 151-158

  • An algorithm is described for fitting the DEDICOM model for the analysis of asymmetric data matrices. This algorithm generalizes an algorithm suggested by Takane in that it uses a damping parameter in the iterative process. Takane's algorithm does not always converge monotonically. Based on the generalized algorithm, a modification of Takane's algorithm is suggested such that this modified algorithm converges monotonically. It is suggested to choose as starting configurations for the algorithm those configurations that yield closed-form solutions in some special cases. Finally, a sufficient condition is described for monotonic convergence of Takane's original algorithm.

  • 4 - Quadratic Functions

  • from Part II - From General Mathematical Background to General Nonlinear Programming Problems (NLP)
  • Vassilios S. Vassiliadis, University of Cambridge, Walter Kähm, Ehecatl Antonio del Rio Chanona, Imperial College London, Ye Yuan
  • Book:
    Optimization for Chemical and Biochemical Engineering
    Published online:
    17 December 2020
    Print publication:
    14 January 2021, pp 44-56

  • Summary

    Quadratic multidimensional functions play a very important role in the understanding of general nonlinear functions. Convexity of quadratic functions is linked in a natural way from its geometrical definition all the way to the properties of its matrix eigenspectrum.Indeed, to second order expansion, and close to the expansion point, any nonlinear function can be approximated by a quadratic – thus providing a crucial link and understanding of the local behaviour and convexity properties of general functions.