Search results
Results From The WOW.Com Content Network
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
A related problem is the ideal membership problem, which consists in testing if a polynomial belongs to an ideal. For this problem also, a solution is provided by an upper bound on the degree of the g i. A general solution of the ideal membership problem provides an effective Nullstellensatz, at least for the weak form.
An alternative approach, e.g., defining the normal matrix as = of size , takes advantage of the fact that for a given matrix with orthonormal columns the eigenvalue problem of the Rayleigh–Ritz method for the matrix = = can be interpreted as a singular value problem for the matrix . This interpretation allows simple simultaneous calculation ...
Torque-free precessions are non-trivial solution for the situation where the torque on the right hand side is zero. When I is not constant in the external reference frame (i.e. the body is moving and its inertia tensor is not constantly diagonal) then I cannot be pulled through the derivative operator acting on L.
Macaulay's resultant is a polynomial in the coefficients of these n homogeneous polynomials that vanishes if and only if the polynomials have a common non-zero solution in an algebraically closed field containing the coefficients, or, equivalently, if the n hyper surfaces defined by the polynomials have a common zero in the n –1 dimensional ...
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
If M is such that LCP(q, M) has a solution for every q, then M is a Q-matrix. If M is such that LCP(q, M) have a unique solution for every q, then M is a P-matrix. Both of these characterizations are sufficient and necessary. [4] The vector w is a slack variable, [5] and so is generally discarded after z is found. As such, the problem can also ...
This is an illustration of the closest vector problem (basis vectors in blue, external vector in green, closest vector in red). In CVP, a basis of a vector space V and a metric M (often L 2) are given for a lattice L, as well as a vector v in V but not necessarily in L. It is desired to find the vector in L closest to v (as measured by M).