Category: Numerical method.

Uniform Approximation

The subject of uniform approximation is distinctly more complicated than that of least-squares approximation. So, we will not devote too…

An Example Of Orthogonal Polynomial Least-Squares Approximation

Chebyshev polynomials of the first kind, and Legendre polynomials are both orthogonal on [−1, 1], but their weighting functions are…

Hermite Polynomials

Condition Numbers

In the previous section there appears to be a problem involved in accurately computing the inverse of R (Hilbert matrix).…

Least-Squares Approximation And Ill-Conditioned Linear Systems

Linear Systems of Equations

Introduction The necessity to solve linear systems of equations is commonplace in numerical computing. This chapter considers a few examples…

Asymptotic Series

The Taylor series expansions of Section 3.5 might have a large radius of convergence, but practically speaking, if x is…

Taylor Series

Fourier Series

The Fourier series expansion was introduced briefly in Chapter 1, where the behaviour of this series with respect to its…

Pointwise Convergence And Uniform Convergence

The previous section informed us that sequences can converge in different ways, assuming that they converge in any sense at…

Sequences and Series

Introduction Sequences and series have a major role to play in computational methods. In this chapter we consider various types…

Number Representations

Introduction In this chapter we consider how numbers are represented on a computer largely with respect to the errors that…