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Ogata Lab
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The lab uses Sato hyperfunctions and complex functions to open new frontiers in numerical analysis.
AboutAbout the lab
Creating numerical analysis
The Ogata Lab studies numerical analysis.
Numerical analysis has a strong practical side, as it studies methods for scientific and technical computing, but it is also a field that is interesting in itself as mathematics.
Under the concept of "creating numerical analysis," the lab uses mathematics and computers to solve a variety of problems and takes on the challenge of opening new frontiers in numerical analysis.
The lab works on numerical computation methods that use the theory of Sato hyperfunctions and complex function theory.
Key terms
- Sato hyperfunction
- A function with singularities, such as poles, discontinuities, or the delta function, represented by complex analytic functions.
- Analytic function
- A function also called a holomorphic function in complex function theory. It has the property that the values at points far apart are closely linked.
- Fourier transform
- A transform used in Fourier analysis, which is important in scientific and technical research. It is hard to compute with conventional numerical integration formulas.
ResearchResearch themes
The Ogata Lab uses mathematics and computers to solve a variety of problems and takes on the challenge of opening new frontiers in numerical analysis. In numerical methods based on the theory of Sato hyperfunctions, computations that are difficult with real numbers are carried out with complex numbers, where they are easier to handle, and the results are then reflected back into the world of real numbers.
*Illustrative imageNumerical Analysis Based on the Theory of Sato Hyperfunctions
Functions with singularities are hard to handle in numerical computation, so the lab uses the idea of Sato hyperfunctions, which represent them with analytic functions, to study numerical integration formulas (the hyperfunction method).
*Illustrative imageNumerical Computation of the Fourier Transform
Because the Fourier transform is hard to compute with conventional numerical integration formulas, the lab devised a numerical method that applies the theory of Sato hyperfunctions. It numerically finds an analytic function and computes the Fourier transform as the difference of its boundary values.
MembersFaculty
The Ogata Lab's members consist of faculty and undergraduate students.
- ProfessorHidenori Ogata
VoicesStudent voices
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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: “Complex Gamma Function” Naitronbomb / CC0 (cropped)
- Numerical Analysis Based on the Theory of Sato Hyperfunctions: “The N function in the complex plane” A1E6 / CC BY-SA 4.0 (cropped)
- Numerical Computation of the Fourier Transform: “Fourier Series-Square wave 3 H” Saisundar.s / CC BY-SA 4.0 (cropped)
- Related lab (Amano Lab): “The Tokyo Stock Exchange - main room 4” Kakidai / CC BY-SA 4.0 (cropped)
- Related lab (Marugame Lab): “Differential geometry of manifolds of figures 1971 cover” 作者不詳 / Public domain (cropped)
- Related lab (Saito Lab): “Two-phase flow types” MichaelFYP / CC BY-SA 4.0 (cropped)
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