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  • 1
    Electronic Resource
    Electronic Resource
    An improved numerical method to find parameters using experimental data (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2851-2860 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we describe a numerical method to determine adjustable parameters in a mathematical model using experimental data. This is basically an improvement over our earlier method which was based on the idea that the area under the experimental curve must be equal to the integral of the function used. The improvement used is the addition of an area correction factor which estimates the necessary difference that must exist between the numerically evaluated and the true area. This correction surprisingly eliminates the use of integral with the result that the two areas being equalized are both numerically evaluated, one using the experimental data points and the other using the fitted function values. It is shown that the application of the area correction factor significantly improves the accuracy of the adjusted parameters. The method has been compared with the well-known method of least squares for few selected cases involving variety of functions. It is seen that our method shows convergence for a wider range of initial guesses as compared to the method of least squares. The superiority of our method becomes evident when more than two non-linear parameters are involved.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361612
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  • 2
    Electronic Resource
    Electronic Resource
    Method to determine optimum number of knots for cubic splines (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 483-488 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new method has been presented to determine the optimum number of knots for cubic splines. The knot-finding process is based on the numerical integration of the input curve. The number and the location of the knots is determined automatically. The method has been applied to a test case and the performance has been compared with two other existing methods. It is shown that fewer knots are retained for the portions of the curve having small curvature whereas a larger number of knots is retained for highly curved portions. The computer time required by our method depends only upon the number of points in the input curve and does not depend upon the shape of the curve or the desired accuracy.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090605
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  • 3
    Electronic Resource
    Electronic Resource
    A numerical approach to find parameters using experimental data (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 7 (1991), S. 259-263 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical technique is presented to determine the unknown parameters in a given relationship using the experimental data. In this technique we formulate the required number of independent relationships by integration applied to various parts of the data along with the criterion of the least-squares error with respect to one parameter. The results for two sample systems, one with two parameters and the other with three parameters, are presented. Comparison with the published work shows that the proposed method is less sensitive to the inaccuracies in the experimental data and generates a better fit than the existing methods such as the ordinary least-squares technique. The method can easily be extended to systems with any number of parameters.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630070402
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