Sentence examples for kernel problems from inspiring English sources

As for the inverse kernel problems related to the integro-differential equation, in [16] [19] efficient strategies to prove the existence and uniqueness of inverse memory kernel problems were given.

Finally, our method in discussing the uniqueness of our inverse problem is different from those inverse memory kernel problems, in which the methods on the basis of the analytic semigroup theory were used.

In order to determine the weakly singular term, we only use the measurement data at a fixed point x 0 ∈ Ω, rather than the usual measurement data on the whole or part of Ω in previous studies of inverse kernel problems.

In this paper we study an inverse weakly singular memory kernel problem for an integro-differential equation related to the Basset problem.

Despite their seemingly different problem formulation, it is shown that both methods can be reduced to the same mathematical kernel problem, i.e. finding the closest (in a certain sense) weighted low rank matrix approximation where the weight is derived from the distribution of the errors in the data.

Lorenzi and Rocca [18] studied an inverse two memory kernels problem in a hyperbolic phase-field model.

Three efficient optimization algorithms are proposed to solve the corresponding kernel learning problems.

The kernel integration problem is often reduced to a convex optimization problem.

In order to overcome the problem of linearity, Schölkopf et al. [ 49] considered nonlinear component analysis as a "kernel eigenvalue problem" and introduced the term "kernel PCA".

Eq. (2) can be converted into the kernel eigenvalue problem: Nlambda a= Ka, (5).

The other approaches like Multiple Kernel Learning MKLL) and deep core vector machines solve the fixed kernel computation problem and scalability aspects of MKMs respectively.