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2 results

  • 8 - A System of Linear Equations and Least Squares Method

  • Chunyan Li, Louisiana State University
  • Book:
    Time Series Data Analysis in Oceanography
    Published online:
    21 April 2022
    Print publication:
    05 May 2022, pp 143-164

  • Summary

    The objective of this chapter is to prepare for the use of MATLAB to find solutions for a system of linear equations. The important concepts include the inverse matrix, solution of a system of linear equations, least squares method, and MATLAB’s “left-division,” which is essentially an implementation of the least squares method. MATLAB functions are very useful and efficient in the job. For real problems, the equations are often highly overdetermined, which occurs when there are many more equations (or measurements) than the number of unknowns, and thus it requires the use of the least squares method to solve the solution in a statistical sense. The contents in this chapter lay out a foundation for several later chapters because many theories and methods are related in one way or the other to the solution of a system of linear equations, e.g. Fourier analysis and harmonic analysis.

  • SYMMETRY RESULT FOR SOME OVERDETERMINED VALUE PROBLEMS

  • Part of
  • MOHAMMED BARKATOU, SAMIRA KHATMI
  • Journal:
    The ANZIAM Journal / Volume 49 / Issue 4 / April 2008
    Published online by Cambridge University Press:
    01 April 2008, pp. 479-494
    • Article
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  • The aim of this article is to prove a symmetry result for several overdetermined boundary value problems. For the two first problems, our method combines the maximum principle with the monotonicity of the mean curvature. For the others, we use essentially the compatibility condition of the Neumann problem.