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Least-Squares Methods

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Abstract

Least-squares is described as a method for solving problems where there is an excess of information available. This is often the case in experimental mechanics. The method can be used to include information from different sources; experimental and theoretical. The method is applied to curve fitting problems and to more general situations. Nonlinear least squares methods are described for fitting of approximation functions.

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References

  1. Leland, O.M., Practical Least Squares, McGraw-Hill, New York, NY (1921)

    MATH  Google Scholar 

  2. Sears, F. W., and Zemansky, M. W., College Physics, Part I, Mechanics, Heat, and Sound, Addison Wesley, Cambridge, MA (1952), p. 59

    Google Scholar 

  3. Dally, J.W., and Riley, W.F., “Experimental Stress Analysis”, McGraw-Hill, New York, NY (1978), Chapter 10

    Google Scholar 

  4. Hamming, R. W., Numerical Methods for Scientists and Engineers, McGraw-Hill, New York, NY (1962), p. 244–246

    MATH  Google Scholar 

  5. Ibid, p. 361,362

    Google Scholar 

  6. Berghaus, D.G., Calculations for Experimental Stress Analysis Using the Personal Computer, Society for Experimental Mechanics., Bethel, CT, (1987), p. 34–36

    Google Scholar 

  7. Businger, P., and Golub, G.H., “Linear Least Squares Solutions Using Householder Transformations”, Numerische Mathematik, 7, (1965), p. 269–276

    Article  MathSciNet  MATH  Google Scholar 

  8. Frocht, M.M., “Photoelasticity, 2”, John Wiley and Sons, New York, NY, (1948), p. 125–129

    Google Scholar 

  9. Berghaus, D.G., “Overdetermined Photoelastic Solutions Using Least- Squares”, Experimental Mechanics, 13, (1973), pp. 97–104

    Article  Google Scholar 

  10. Berghaus, D.G., and Aderholdt, R.E., “Photoelastic Analysis of Interlaminar Matrix Stresses in Fibrous Composite Models”, Experimental Mechanics, 15, (1975), p. 409–417

    Article  Google Scholar 

  11. Doyle, J.F., and Danyluk, H.T., “Integrated Photoelasticity for Axisymmetric Problems”, Experimental Mechanics, 18, (1978), p. 215–220

    Article  Google Scholar 

  12. Berghaus, D.G., “Combining Photoelasticity and Finite-element Methods for Stress Analysis Using Least-Squares, Experimental Mechanics, 31, (1991), p. 36–41

    Article  Google Scholar 

  13. Berghaus, D.G., “Adding the LaPlace Equation to Least Squares Photoelastic Stress Solutions”, Experimental Techniques, 13, (1989), p. 18–21

    Article  Google Scholar 

  14. Daniel, D., and Wood, F.S., Fitting Equations to Data, Wiley-Interscience, New York, NY (1971), Chapter 3

    MATH  Google Scholar 

  15. Berghaus, D.G., “Fitting of Simple Approximation Functions Using Nonlinear Least Squares Methods”, Experimental Mechanics, 17, (1977), p. 14–20

    Article  Google Scholar 

  16. Woods, T.O., and Berghaus, D.G. “The Biaxial Loading Response of Powder Aluminum atElevated temperature”, Experrimental Mechanics, 34 (1994), p 249–255

    Article  Google Scholar 

  17. Woods, T.O., Berghaus, D.G., and Peacok, H.B., “Interparticle Movement and the Mechanical Behavior of Extruded Powder Aluminum at Elevated Temperature”, Experimental Mechannics, 38, (1998), p. 110–115

    Article  Google Scholar 

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© 2001 Springer Science+Business Media New York

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Berghaus, D. (2001). Least-Squares Methods. In: Numerical Methods for Experimental Mechanics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1473-2_2

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  • DOI: https://doi.org/10.1007/978-1-4615-1473-2_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-7403-9

  • Online ISBN: 978-1-4615-1473-2

  • eBook Packages: Springer Book Archive

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