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Tanaka Lab
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A lab that mathematically designs formulas for function approximation and numerical integration.
AboutAbout the lab
Exploring numerical methods and their mathematics
The Tanaka Lab studies numerical analysis and the computational methods used in science and engineering.
The lab mathematically designs formulas that approximate functions well and formulas that compute integrals numerically.
In doing so, it draws on ideas from optimization, for example using mathematical optimization to decide at which points to take the function's values.
The lab's research also covers numerical computation for economics and finance, and verified numerical computation, which guarantees bounds on the error.
Key terms
- numerical analysis
- The branch of mathematics concerned with methods for solving, approximately on a computer, problems that cannot be solved in closed form, and with analyzing the errors of those methods
- numerical integration
- A method of approximately computing the value of an integral by combining the function's values at several points
- mathematical optimization
- Mathematically finding the choice that makes a quantity smallest (or largest) under given conditions
NewsLab news
A paper on sparse solutions of kernel herding was published
A paper by Prof. Tanaka and colleagues received the Paper Award of the Japan Society for Industrial and Applied Mathematics
A paper on methods for computing the matrix exponential was published in an applied mathematics journal
A paper on lower bounds for the error of numerical integration was published in a SIAM journal
ResearchResearch themes
The lab studies numerical analysis and computational methods for science and engineering. Centered on function approximation, numerical integration, and the mathematical optimization that supports them, its work extends to applications to equations, numerical computation for economics and finance, and verified numerical computation.
*Illustrative imageChoosing sample points and discretizing measures
In interpolation and numerical integration, the points at which the function's values are used determine accuracy. The lab studies methods for finding good sample points in a variety of settings by using mathematical optimization to minimize a quantity that evaluates the placement of the points.
*Illustrative imageApproximation formulas for analytic functions
The lab studies methods for handling analytic functions, which are fundamental to scientific and technical computing, numerically by using variable transformations. The core of this work is numerical integration based on the double exponential (DE) transformation and function approximation using sinc functions.
*Illustrative imageOptimizing variable transformations
This research improves the DE transformation itself. Based on the locations of the function's singularities, it constructs a mapping with the Schwarz-Christoffel transformation to obtain better approximation formulas.
*Illustrative imageNumerical computation for economics and finance
The lab works on numerical methods related to economics and finance. The focus is on methods for computing functionals of the stochastic processes used in those fields, and this is also a thesis topic for undergraduate and graduate students.
MembersFaculty
- ProfessorKen'Ichiro TanakaPublications ↗
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Domain coloring x2-1 x-2-i x-2-i d x2+2+3i” Djiboun / CC BY-SA 4.0 (cropped)
- Choosing sample points and discretizing measures: “Chebyshev nodes from the circle” Jacobolus / CC BY-SA 4.0 (cropped)
- Approximation formulas for analytic functions: “Sinc function (neutral)” 作者不詳 / Public domain (cropped)
- Optimizing variable transformations: “Звезда внутри интеграл Шварца-Кристоффеля” Newhydro / CC BY-SA 4.0 (cropped)
- Numerical computation for economics and finance: “Market centre in Tokyo stock exchange” ehnmark / CC BY 2.0 (cropped)
- Related lab (中野張研究室): “Brownian surface” Prokofiev / CC BY-SA 3.0 (cropped)
- Related lab (鹿島亮研究室): “Formulas on an old blackboard (Unsplash)” Roman Mager roman_lazygeek / CC0 (cropped)
- Related lab (西畑伸也研究室): “Collision de solitons hydrodynamiques” Christophe.Finot, Julien Fatome, Stéphane Pitois / CC BY-SA 4.0 (cropped)
- Related lab (山下真研究室): “Rosenbrock function 2” RokerHRO / Public domain (cropped)
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