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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

1996 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I 1996 • Question 6

Least Squares. Describe in general the problem of approximating a given function in the Least Squares sense by a linear combination of certain basis functions. Discuss the significance of orthogonal basis functions. If you have a basis that is not orthogonal, how can you obtain an orthogonal basis that spans the same space?

Raw LaTeX

\textbf{Least Squares.} Describe in general the problem of approximating a given
function in the Least Squares sense by a linear combination of certain basis
functions. Discuss the significance of orthogonal basis functions. If you have a
basis that is not orthogonal, how can you obtain an orthogonal basis that spans the
same space?

Topic Tags

Least Squares and Normal Equations Linear Programming and Optimization Orthogonal and Unitary Matrices Projectors and Orthogonal Projections