Research Topics
- Self-Validating Methods, Numerical Verification Methods
Validated numerics
is developed and expected to bridge the gap between a numerically observed
phenomenon, and its mathematical counter-part. Main techniques and tools
in this field are interval arithmetic, floating-point computations with
switching rounding mode, symbolic approaches, formal proofs and so on.
- Wavelet Analysis and its application
The wavelet transform is widely used in many fields such as signal processing,
image processing and numerical computation of differential equations.
Wavelet analysis theory is still ongoing and applied to many fields.
Both wavelets and validated numerics are powerful tools in applied mathematics
with applications such as image processing and numerical simulation. However,
wavelets are not well known in the field of validated numerics and vice
versa at the present. We explore new possibilities for wavelet and numerical
analysis. The scopes will cover all the aspects of Wavelet and Numerical
Analysis, with theories, methods, and applications.
