Predicate Encryption Supporting Disjunctions, Polynomial Equations, and Inner Products
As a matter of fact, several inner products
are to be defined when considering the inverse optimization problem.
Moreover, general inner products
are considered, which facilitate the incorporation of arbitrary preconditioners and allow to exploit the self-adjointness of a problem algorithmically when its natural inner product
According to equation (1), all of the inner products
in Table 6 are shown as below:
It is shown that introducing this latter makes the calculation of inner products
analytical in one hand and ensures unconditional stability on the other hand; on the contrary to our first implementation.
Sanz-Serna: On polynomials orthogonal with respect to certain Sobolev inner products
The core of the book presents an axiomatic development of the most important elements of finite-dimensional linear algebra: vector spaces, linear operators, norms and inner products
, and determinants and eigenvalues.
For the subclass J P (X), of all inner products
defined on X, of H(X) and y [not equal to] 0, we may define
However, not all kernels correspond to inner products
in some feature space F could be used.
Kernels are inner products
in some space but not necessarily in the space where the input data come from.
If D is integrally representable and if D' is an integral representation of D, then, inner products
of pairs of vectors in D' are integers.
The second procedure uses only definite (discrete) inner products
and is conceptually much simpler, but has difficulty with poles very close to the interval of integration, which cause convergence to slow down.