The translator writing system in its didactic version is an ideal tool upon which a course on compiler construction can be based. The student can treat non-trivial examples in a flexible and modular way within a reaso...
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An adaptive quadrature method for the automatic computation of integrals with strongly oscillating integrand is presented. The integration method is based on a truncated Chebyshev series approximation. The algorithm u...
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A nonadaptive automatic integration scheme using Clenshaw-Curtis quadrature is presented. Extensions are made to calculate Cauchy principal values and integrals having algebraic and logarithmic end point singularities...
Lower and upper bounds are determined for the conditioning of triangular and trapezoid matrices of full rank. These bounds can justify column pivoting in Gaussian elimination and in orthogonal elimination, or symmetri...
Lower and upper bounds are determined for the conditioning of triangular and trapezoid matrices of full rank. These bounds can justify column pivoting in Gaussian elimination and in orthogonal elimination, or symmetrical pivoting in Cholesky factorization, or singular value decomposition instead of elimination.
Equivalent inherent rounding errors (E.I.R.E.) are defined as perturbations on the given data, such that the computed solution is the exact solution of the problem with perturbed data. Almost minimal E.I.R.E. are comp...
Equivalent inherent rounding errors (E.I.R.E.) are defined as perturbations on the given data, such that the computed solution is the exact solution of the problem with perturbed data. Almost minimal E.I.R.E. are computed for solutions of consistent sets of linear equations (with one or more right hand sides). Non consistent sets are also treated, but their computed E.I.R.E. cannot be proven almost minimal in all cases.
A numerical method for the solution of the Abel integral equation is presented. The known function is approximated by a sum of Chebyshev polynomials. The solution can then be expressed as a sum of generalized hypergeo...
A numerical method for the solution of the Abel integral equation is presented. The known function is approximated by a sum of Chebyshev polynomials. The solution can then be expressed as a sum of generalized hypergeometric functions, which can easily be evaluated, using a simple recurrence relation.
Recurrence formulas for the calculation of the modified moments $$\int\limits_{ - 1}^{ + 1} {(1 - x)^\alpha (1 + x)^\beta T_n (x)dx} $$ ...
Recurrence formulas for the calculation of the modified moments
$$\int\limits_{ - 1}^{ + 1} {(1 - x)^\alpha (1 + x)^\beta T_n (x)dx} $$
and
$$\int\limits_{ - 1}^{ + 1} {(1 - x)^\alpha (1 + x)^\beta \ln \left( {\frac{{1 + x}}{2}} \right)T_n (x)dx} $$
are presented. Some applications of these modified moments are discussed, such as the numerical calculation of integrals of functions having branch points, the computation of Chebyshev series coefficients and the construction of Gaussian quadrature formulas for integrals with logarithmic singularity.
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