Related papers: Yet another DE-Sinc indefinite integration formula
The Sinc convolution is an approximate formula for indefinite convolutions proposed by Stenger. The formula was derived based on the Sinc indefinite integration formula combined with the single-exponential transformation. Although its…
The Sinc approximation is known to be a highly efficient approximation formula for rapidly decreasing functions. For unilateral rapidly decreasing functions, which rapidly decrease as $x\to\infty$ but does not as $x\to-\infty$, an…
F. Stenger proposed efficient approximation formulas for derivatives over infinite intervals. These formulas were derived by combining the Sinc approximation with appropriate conformal maps. It has been demonstrated that these formulas can…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier integral. The double exponential transformation is not only useful for numerical computations but it is…
This paper is a short introduction to numerical methods using the double exponential (DE) transformation, such as tanh-sinh quadrature and DE-Sinc approximation. The DE-based methods for numerical computation have been developed intensively…
The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation.…
This paper reinforces numerical iterated integration developed by Muhammad--Mori in the following two points: 1) the approximation formula is modified so that it can achieve a better convergence rate in more general cases, and 2) explicit…
While the trapezoidal formula can attain exponential convergence when applied to infinite integrals of bilateral rapidly decreasing functions, it is not capable of this in the case of unilateral rapidly decreasing functions. To address this…
The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…
The Sinc approximation has shown high efficiency for numerical methods in many fields. Conformal maps play an important role in the success, i.e., appropriate conformal map must be employed to elicit high performance of the Sinc…
We propose and analyze a symmetric version of the Zassenhaus formula for disentangling the exponential of two non-commuting operators. A recursive procedure for generating the expansion up to any order is presented which also allows one to…
We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, the convergence has already been…
The integration operators (*) $({\mathcal J}^+\,g)(x) = \int_a^x g(t) \, dt$ and (**) $({\mathcal J}^-\,g)(x) = \int_x^b g(t) \, dt$ defined on an interval $(a,b) \subseteq {\mathbf R}$ yield new identities for indefinite convolutions,…
The double exponential formula, or the DE formula, is a high-precision integration formula using a change of variables called a DE transformation; whereas there is a disadvantage that it is sensitive to singularities of an integrand near…
Two representations of the extended gamma functions $\Gamma^{2,0}_{0,2}[(b,x)]$ are proved. These representations are exploited to find a transformation relation between two Fox's $H$-functions. These results are used to solve Fox's…
A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating…
We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms…
We propose a method for designing accurate interpolation formulas on the real axis for the purpose of function approximation in weighted Hardy spaces. In particular, we consider the Hardy space of functions that are analytic in a strip…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…