where A is a 4*3 non-rectangular matrix, x is the 3*1 unknown vector and b is the 3*1 vector. I know if the minimum two norm sum of x, i.e. sqrt(x(1)^2+x(2)^2+x(3)^2), is wanted, then the solution is x=pinv(A)*b, where pinv(A) is the pseudo-inverse matrix ...
Given a symmetric positive-definite matrix A, the number of iterations needed to reduce the norm of the residual by a constant factor is bounded by the spectral condition number of A. The spectral condition number [kappa](A) is the ratio of the extreme eigenvalues of A, [kappa](A) = [...
Furthermore, if v represents a vector, ‖v‖ represents the l2 or l∞ norm of the vector v. RQSGD By quantizing full-precision floating-point numbers, the communication cost of distributed and federated learning can be significantly reduced. The quantization process of RQSGD consists of two ...
The vector-valued $T(1)$ theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency s... Tuomas P. Hytnen - 《Bulletin of the Polish Academy of Sciences Mathematics》 被引量: 11发表: 2011年 Two weight Sobolev norm ineq...
(optional) $sDratios shear distances from iNode as a fraction of the element length, size of ratio vector is 1 for 2D-case and 2 for 3D-case (entries: [dy_iNode, dz_iNode] (optional, default = [0.5 0.5]) -doRayleigh to include Rayleigh damping from the element (optional, default =...
The Euclidean space Rn+1 is identified with the subset of the Clifford algebra Rn consisting of the so-called paravectors via the map (x0,x1,…,xn)⟼x=x0+x_=∑i=0neixi. For a paravector x≠0, its norm is given by |x|=(xx¯)1/2, its conjugate by x¯=x0−∑i=1ne...
In order to improve the performance of IWTDLMS-SA, the variable step-size IWTDLMS-SA (VSS-IWTDLMS-SA) is introduced. The VSS-IWTDLMS-SA is derived by minimizing the \\(\\ell _1\\)-norm of the a posteriori error vector. To increase the tracking ability of the VSS-IWTDLMS-SA, the...
In the ABP, fi is given by a vector of fixed norm: fi = U0nˆi, where nˆi = (cosθi, sinθi) is a unit vector whose angle, θi, evolves as a Wiener process $${\dot{\theta }}_{i}=\sqrt{2{D}_{r}}{\xi }_{i}.$$ (3) The constant Dr is the ...
Note that the two input vectors do not have to be normalized, and do not need to have the same norm.void ImuTracker::AddImuLinearAccelerationObservation( const Eigen::Vector3d& imu_linear_acceleration) { // Update the 'gravity_vector_' with an exponential moving average using the ...
Let $R$ be the vector of Riesz transforms on $\\mathbb{R}^n$, and let $\\mu,\\lambda \\in A_p$ be two weights on $\\mathbb{R}^n$, $1 < p < \\infty$. The two-weight norm inequality for the commutator $[b, R] : L^p(\\mathbb{R}^n;\\mu) o L^p(\\mathbb{R}...