Uniform Approximation
The subject of uniform approximation is distinctly more complicated than that of least-squares approximation. So,…
Numerical method
Numerical method
An Example Of Orthogonal Polynomial Least-Squares Approximation
Chebyshev polynomials of the first kind, and Legendre polynomials are both orthogonal on [−1, 1],…
Numerical method
Condition Numbers
In the previous section there appears to be a problem involved in accurately computing the…
Numerical method
Linear Systems of Equations
Introduction The necessity to solve linear systems of equations is commonplace in numerical computing. This…
Numerical method
Asymptotic Series
The Taylor series expansions of Section 3.5 might have a large radius of convergence, but…
Numerical method
Fourier Series
The Fourier series expansion was introduced briefly in Chapter 1, where the behaviour of this…
Numerical method
Pointwise Convergence And Uniform Convergence
The previous section informed us that sequences can converge in different ways, assuming that they…