What mathematical analysis is commonly used to predict tides?

Harmonic or Fourier analysis is the correct choice because it is specifically designed to analyze periodic functions, such as tidal patterns. Tides are influenced by gravitational forces exerted by the moon, sun, and other celestial bodies, which create complex, periodic fluctuations in sea levels.

Harmonic analysis involves breaking down these tidal signals into their constituent sine and cosine components, allowing for a more accurate prediction of future tide levels based on past data. This method takes into account the predictable cyclical nature of tides, making it possible to model tidal heights and times with high precision.

Other analytical methods, while useful in various contexts, do not address the specific periodicity and complexity inherent in tidal phenomena. For example, algebraic analysis focuses on solving equations and inequalities but does not directly relate to cyclical patterns. Geometric analysis pertains more to spatial relationships and shapes rather than periodic functions like tides. Linear regression can model relationships between variables but is less suited for capturing the periodic nature of tide data compared to harmonic or Fourier analysis. Thus, harmonic analysis is the most accurate and commonly used method for tidal prediction.