To assess the relaxivity of our particles, we used a benchtop relaxometer (mq60 "The Minispec", from Bruker) with field strength of 1.41 T. For each synthesized batch, 2000 times diluted samples were prepared in Milli-Q water; dilutions were in triplicate, such to minimize approximation errors.
In this section, we consider the waveform design problem by minimizing approximation error accounting for constant modulus and similarity constraints.
K-SVD uses a different strategy such that the columns of A are updated sequentially one at a time by using an SVD to minimize the approximation error.
A SVM is a machine learning technique that does not minimize an approximation error considering a dataset, but maximizes the distance between the clusters that are to be classified.
where,, are optimal unknown (constant) weights that minimize the approximation error over,,, are a set of basis functions such that each component of takes values between 0 and 1,,, are the modeling errors, and, where,, are bounds for the optimal weights,.
Conventional parameter estimation approaches seek parameter values that minimize the approximation error assuming a given regulatory scheme (i.e., fixing some f r,j to zero beforehand according to the aprioristic biochemical knowledge of the system).
The problem becomes looking only at the training vectors that uses only one column of the dictionary vector in its approximation, minimizing the approximation error E k.
We propose an efficient algorithm to compute the optimal value of the shape parameter that minimizes the approximation error.
Most of these methods focus on minimizing the approximation error; however, they usually result in a loss of physical interpretability of the reduced model.
Obtaining the parameters that yield the approximation of a particular function depends on a supervised learning algorithm, generally using a gradient descendent approach that iteratively minimizes the approximation error for a given dataset, but often leads to local minima [33].
