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2 results

  • 11 - Data Analysis: Curve Fitting and Interpolation

  • from Part III - Least Squares and Optimization
  • Kevin W. Cassel, Illinois Institute of Technology
  • Book:
    Matrix, Numerical, and Optimization Methods in Science and Engineering
    Published online:
    18 February 2021
    Print publication:
    04 March 2021, pp 560-593

  • Summary

    Analysis of various data sets can be accomplished using techniques based on least-squares methods.For example, linear regression of data determines the best-fit line to the data via a least-squares approach.The same is true for polynomial and regression methods using other basis functions.Curve fitting is used to determine the best-fit line or curve to a particular set of data, while interpolation is used to determine a curve that passes through all of the data points.Polynomial and spline interpolation are discussed.State estimation is covered using techniques based on least-squares methods.

Matrix, Numerical, and Optimization Methods in Science and Engineering
  • Kevin W. Cassel
  • Published online:
    18 February 2021
    Print publication:
    04 March 2021
  • Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.