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Kashiwagi Lab
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A lab studying verified numerical computation, which guarantees that the results of computer calculations are correct.
AboutAbout the lab
Guaranteeing reliable answers from computer calculations
Kashiwagi Lab studies verified numerical computation, which guarantees that the results of numerical computation are correct.
The lab works on methods for finding all solutions of multivariable equations, and on interval arithmetic, a way of computing with ranges.
It also studies methods for computing solutions of ordinary differential equations with mathematically guaranteed accuracy.
Key terms
- verified numerical computation
- A method of computation that mathematically guarantees that the result computed on a computer lies within a range containing the correct answer
- interval arithmetic
- A way of computing in which a number is represented not by a single value but by a range (interval) that is certain to contain it
- nonlinear equation
- A complex equation in which the relationships between variables cannot be expressed in a simple form such as proportionality
ResearchResearch themes
The lab studies verified numerical computation, which mathematically guarantees that the results of numerical computation on computers are correct.
*Illustrative imageFinding all solutions of nonlinear equations
The lab studies methods for finding every possible solution of multivariable nonlinear equations. A key challenge is how to reduce the computational cost.
*Illustrative imageNew interval arithmetic methods
This research is closely related to the all-solutions search methods. The lab studies forms of interval arithmetic that can determine guaranteed ranges more efficiently.
*Illustrative imageVerified linear programming
As an application of interval arithmetic, the lab studies solution methods that use linear programming. It aims to develop methods for solving linear programming itself with guaranteed accuracy.
*Illustrative imageVerified computation for ordinary differential equations
By using special operations on power series, the lab studies methods for computing solutions of ordinary differential equations efficiently with guaranteed accuracy.
MembersFaculty
The members of Kashiwagi Lab are faculty, master's students, and undergraduate students.
- ProfessorMasahide Kashiwagi
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: “Convergence of Iterative Numerical Methods for Poisson System with 16384 elements” ansariddle / CC BY-SA 4.0 (cropped)
- Finding all solutions of nonlinear equations: “Nonlinear Pendulum Solutions for Different Initial Amplitudes” Tomasz59 / CC BY-SA 4.0 (cropped)
- New interval arithmetic methods: “Murray Star Maze in spring” Роман Рябенко / CC0 (cropped)
- Verified linear programming: “Simplex algorithm” Lorepenoten / CC0 (cropped)
- Verified computation for ordinary differential equations: “Advection equation solution comparison” Gigowatts / CC BY-SA 3.0 (cropped)
- Related lab (荻田研究室): “U.s.-kilogram-masses” National Institute of Standards and Technology / Public domain (cropped)
- Related lab (劉研究室): “Triangular wave and square wave on oscilloscope screen (cropped)” User:Xato / CC0 (cropped)
- Related lab
(早水研究室): “Petersen graph total coloring” Vinod kalagi / CC BY-SA 4.0 (cropped) - Related lab (大本研究室): “Ripples dispersing sunlight into underwater rainbows in Brofjorden” W.carter / CC BY-SA 4.0 (cropped)
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