Linear Least-Squares Approximation

Discrete Data - Orthogonal Basis Polynomials - Continuous Data


■ Specific Sources

! Script Least-Squares Approximation           Script MinMax Approximation (Chebyshev)

Bronstein: Section 19.6.2

Least-Squares: http://en.wikipedia.org/wiki/Least_squares
Linear Least-Squares: http://en.wikipedia.org/wiki/Linear_least_squares
Gram-Schmidt Procedure: http://en.wikipedia.org/wiki/Gram-Schmidt


■ Teaching Material for the Classroom (Mathematica Notebooks, Exercises, Demos etc.)

Mathematica-Notebook Linear Least-Squares: LeastSquares1.nb
Mathematica-Notebook and Excel-File with Example from Lecture1 cont.: Case_Durchfluss.zip

Mathematica-Notebook with 3d example: Case_Hand3DLeastSquares.nb and 3d point set as .txt file pointsall.txt

! Exercises 6     and     ! Solutions 6
! Exercises 7     and     ! Solutions 7     and     Solutions 7 Figures
! Exercises 8     and     ! Solutions 8


★ Further Topics or Subjects from the Bachelor Degree Program

Nonlinear Least-Squares: Bronstein: Section 19.6.2

Multivariate Least-Squares Approximation: Bronstein: Section 19.6.2

Min-Max-Approximation: Schaum's Outline of Numerical Analysis: Chapter 22
Chebyshev-Approximation (Min-Max): Bronstein: Section 19.6.3

Trigonometric Approximation: Schaum's Outline of Numerical Analysis: Chapter 24
Harmonic Analysis: Bronstein: Section 16.2.4


☆ General Sources (Encyclopedias a.s.o. with prompt or index search)

Mathworld: http://www.mathworld.com
Wikipedia Category of Numerical Analysis: en.wikipedia.org
Springer Encyclopedia of Math Online (Advanced): https://encyclopediaofmath.org