The equation would be: V = A2^(Y/3)
The basic form of an exponential equation is y = ab^x.
The a is the starting amount. In this problem, we don't know that, so we just leave it as a.
The b is the rate. In this case, we are doubling the volume so we times it by 2.
The x is the amount of years. Since it is every 3 years, we can divide the x by 3.
The purpose of the tensor-on-tensor regression, which we examine, is to relate tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without being aware of its intrinsic rank beforehand.
By examining the impact of rank over-parameterization, we suggest the Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN) methods to address the problem of unknown rank. By demonstrating that RGD and RGN, respectively, converge linearly and quadratically to a statistically optimal estimate in both rank correctly-parameterized and over-parameterized scenarios, we offer the first convergence guarantee for the generic tensor-on-tensor regression. According to our theory, Riemannian optimization techniques automatically adjust to over-parameterization without requiring implementation changes.
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