alt="images"/> Table 4.3 Clenshaw–Curtis quadrature approximation of
.Table 4.4 Composite trapezoidal
, Clenshaw–Curtis
, and composite trapezoida...Table 4.5 Cotangent quadrature rule approximation
(4.88) of integral (4.91) ...Table 4.6 Approximation values of integral (4.101) using Fejér's formula (4.9...
4 Chapter 6Table 6.1 Iterates of Newton's methods applied to system (6.21).Table 6.2 Solutions and conditioning of system (6.22).Table 6.3 Iterates of Newton's methods applied to system (6.22).
5 Chapter 8Table 8.1 Leading approximated eigenvalues of boundary value problem (8.42).Table 8.2 Numerical solution of
using different Runge–Kutta methods with
....Table 8.3 Adams–Bashforth normalized coefficients
Table 8.4 Backward difference coefficients
.
List of Illustrations
1 Chapter 1Figure 1.1 (a) A simple exploration of reveals a change of sign within the...Figure 1.2 (a) Analysis of the order of convergence of the Newton's method: ...Figure 1.3 (a) Graph intercepting ordinates and at abscissas and , ...Figure 1.4 (a) Convergence history of Newton's and secant methods when the s...
2 Chapter 2Figure 2.1 Equispaced grid with .Figure 2.2 (a) Trigonometric function (black solid curve) and the interpol...Figure 2.3 Interpolation of the function (solid black curve) using equispa...Figure 2.4 Lebesgue functions associated with sets of equispaced nodes (2....Figure 2.5 Interpolation of with equispaced nodes. (a) (solid black) and...Figure 2.6 Chebyshev nodes (hollow circles) as the horizontal projection of ...Figure 2.7 Lebesgue functions and constants associated with the Chebyshev no...Figure 2.8 Interpolation of the function
(solid black curve) using Chebysh...Figure 2.9 Interpolation of the function using Chebyshev nodes. (a) Pointw... 3 Chapter 3Figure 3.1 Numerical differentiation: starting from the known values
of a ...Figure 3.2 From top to bottom, finite difference formulas (3.3), (3.4), (3.5...Figure 3.3 Centered difference formula (3.5) applied on a set of equidistant... 4 Chapter 4Figure 4.1 Geometrical representation of simple interpolatory quadratures fo...Figure 4.2 Areas associated with the composite trapezoidal rule (hatched reg...Figure 4.3 Areas associated with the composite Simpson's rule (hatched regio...Figure 4.4 Absolute quadrature errors of composite trapezoidal and Simpson r...Figure 4.5 Chebyshev polynomials
(solid black), (dashed black), (solid...Figure 4.6 Absolute quadrature error in the Clenshaw–Curtis quadrature appro...Figure 4.7 Computation of the length of the ellipse . (a) We compute the ...Figure 4.8 Semi‐logarithmic plot of the absolute quadrature errors correspon...Figure 4.9 Cotangent transformation applied on the abscissas (4.89) for Figure 4.10 Absolute quadrature error of cotangent quadrature formula (4.8...Figure 4.11 Hyperbolic tangent transformation applied on the abscissas ....Figure 4.12 Absolute quadrature errors of the approximation of integral (4... 5 Chapter 5Figure 5.1 Linear fitting. The gray disks are the experimental observations....Figure 5.2 The resulting vector
is the reflection of across the line ....Figure 5.3 (a) Properties (5.137). (b) There are two possible reflectors (ac...Figure 5.4 QR‐factorization of a non‐square matrix .Figure 5.5 Classical Gram–Schmidt (CGS) algorithm.Figure 5.6 CGS and QR‐factorization equivalence.Figure 5.7 Near parallelism between and results in a vector with very ... 6 Chapter 6Figure 6.1 Geometrical interpretation of a system of two nonlinear equations...Figure 6.2 (a) Solutions of system (6.21) showing the first three iterates o...Figure 6.3 Parameter‐dependent solution branches of (6.25).Figure 6.4 (a) Rotating pendulum. (b) Trivial solution branch
