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  1. Article

    Correction to: Kernel-based interpolation at approximate Fekete points

    An equation in Section 2.1 has been corrected.

    Toni Karvonen, Simo Särkkä, Ken’ichiro Tanaka in Numerical Algorithms (2021)

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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 ...

    Toni Karvonen, Simo Särkkä, Ken’ichiro Tanaka in Numerical Algorithms (2021)

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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...

    Ken’ichiro Tanaka, Masaaki Sugihara in New Sinc Methods of Numerical Analysis (2021)

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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...

    Ken’ichiro Tanaka in Numerical Algorithms (2020)

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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...

    Ken’ichiro Tanaka, Tomoaki Okayama… in Approximation Theory XV: San Antonio 2016 (2017)

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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...

    Ken’ichiro Tanaka, Tomoaki Okayama, Takayasu Matsuo… in Numerische Mathematik (2013)

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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...

    Tomoaki Okayama, Ken’ichiro Tanaka, Takayasu Matsuo… in Numerische Mathematik (2013)

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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...

    Ken’ichiro Tanaka, Masaaki Sugihara, Kazuo Murota, Masatake Mori in Numerische Mathematik (2009)

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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...

    Ken’ichiro Tanaka, Sunao Murashige, Shin’ichi Oishi in Numerische Mathematik (2004)