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Article
Correction to: Kernel-based interpolation at approximate Fekete points
An equation in Section 2.1 has been corrected.
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Article
Kernel-based interpolation at approximate Fekete points
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error ...
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Chapter
Construction of Approximation Formulas for Analytic Functions by Mathematical Optimization
We describe our methods developed recently to construct formulas for approximating functions and numerical integration. Our methods are developed basically for improving the with variable transformations kno...
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Article
Generation of point sets by convex optimization for interpolation in reproducing kernel Hilbert spaces
We propose algorithms to take point sets for kernel-based interpolation of functions in reproducing kernel Hilbert spaces (RKHSs) by convex optimization. We consider the case of kernels with the Mercer expansi...
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Chapter and Conference Paper
Potential Theoretic Approach to Design of Accurate Numerical Integration Formulas in Weighted Hardy Spaces
We propose a method for designing accurate numerical integration formulas on weighted Hardy spaces, which are regarded as spaces of transformed integrands by some useful variable transformations such as the do...
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Article
DE-Sinc methods have almost the same convergence property as SE-Sinc methods even for a family of functions fitting the SE-Sinc methods
In this paper, the theoretical convergence rate of the Sinc indefinite integration combined with the double-exponential (DE) transformation is given for a class of functions for which the single-exponential (S...
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Article
DE-Sinc methods have almost the same convergence property as SE-Sinc methods even for a family of functions fitting the SE-Sinc methods
In this paper, the theoretical convergence rate of the trapezoidal rule combined with the double-exponential (DE) transformation is given for a class of functions for which the single-exponential (SE) transfor...
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Article
Function classes for double exponential integration formulas
The double exponential (DE) formulas for numerical integration are known to be highly efficient, more efficient than the single exponential (SE) formulas in many cases. Function classes suited to the SE formul...
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Article
On necessary and sufficient conditions for numerical verification of double turning points
This paper describes numerical verification of a double turning point of a nonlinear system using an extended system. To verify the existence of a double turning point, we need to prove that one of the solutio...