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