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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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An efficient variable projection formulation for separable nonlinear least squares problems.

Min Gan, Han-Xiong Li

    IEEE Transactions on Cybernetics
    |July 13, 2013
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces an efficient variable projection algorithm for nonlinear least squares problems. The new method significantly reduces computation time by simplifying the problem using matrix decomposition.

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    Area of Science:

    • Numerical analysis
    • Computational mathematics

    Background:

    • Nonlinear least squares problems are common in various scientific and engineering fields.
    • Existing variable projection algorithms can be computationally intensive.

    Purpose of the Study:

    • To develop a more efficient variable projection algorithm for nonlinear least squares problems.
    • To reduce the computational cost associated with solving these problems.

    Main Methods:

    • Proposing a novel variable projection functional utilizing matrix decomposition.
    • Applying the Levenberg-Marquardt algorithm with finite differences to minimize the new criterion.

    Main Results:

    • The proposed formulation results in a smaller decomposed matrix compared to previous methods.
    • Numerical results demonstrate a significant reduction in computing time.

    Conclusions:

    • The new variable projection functional offers a more efficient approach to solving nonlinear least squares problems.
    • This method provides a substantial improvement in computational efficiency.