As an extension of the matrix inversion lemma, the representation of the pseudoinverse of the sum of two matrices of the form $( S + \Phi \Phi^* )$ with S hermitian is considered by a geometric approach introducing orthogonal projections associated with the orthogonal decomposition of the rel...
matrix inversion lemmaFourier expansion methodKalman filteringIn this paper, the optimal filtering problem for a discrete-time linear distributed parameter system is considered. Using the least squares estimation error criterion, the Wiener-Hopf equation for the discrete-time distributed parameter system is...
The prover needs to compute an ideal corresponding to , and to do this we pull back the kernel of under , compute the ideal and then push forward (via Lemma 3 of the paper). This results in , which is a left--ideal. Now comes the really subtle bit. We have the three isogenies ,...
By applying the matrix inversion lemma (Aˆ+BˆCˆDˆ)−1=Aˆ−1−Aˆ−1Bˆ(Cˆ−1+DˆAˆ−1Bˆ)−1DˆAˆ−1 with Aˆ=Cˆ=I, Dˆ=A, and B=−ak,kIMΔt, the algorithm laid out in Section 1.2.1 may be rewritten in a form that onl...
based on the matrix inversion lemma [34] B - 1 = C + DE D H - 1 = C - 1 - C - 1 D E - 1 + D H C - 1 D - 1 D H C - 1 . (47) The inverse of the matrix D k needs to be expressed in terms of inverse of the covariance matrix Ck-1to obtain iterative energy...
Mathlib.Analysis.Fourier.Inversion Mathlib.Analysis.Fourier.PoissonSummation Mathlib.Analysis.Fourier.RiemannLebesgueLemma Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.FunctionalSpaces.SobolevInequality Mathlib.Analysis.Hofer Mathlib.Analysis.InnerProductSpace.Adjoint Mathlib.Analysis.InnerProductSpace.Basic ...
where\(f_i\)’s are polynomial functions from\({\mathbb F}_{2^n}\)to\({\mathbb F}_2\). According to Lemma1, we may have\(\mathbf{{b}}\cdot F =Tr_1^m(\xi F)\)for some\(\xi \in {\mathbb F}_{2^m}^*\). In particular,\(\mathbf{{b}}\cdot F = Tr_1^m(\beta...
Lemma 2.4 [18, Lemma 4.1] Let u satisfy the initial-boundary value problem (3), where g∈C1[0,T] and f∈L2(Ω). Then the weak solution u is denoted by u=∫0tθ(t−τ)v(τ)dτ,0<t<T, (9) where θ∈L1(0,T), J1−αθ=g(t). v is the solution to the followi...
Lemma 2.6Let p be a prime such that \({\widetilde{X}}\) is smooth over \({\mathbb {Z}}_p\). On \(\omega _X^{-l}\), the p-adic norm \(\Vert \cdot \Vert _p\) defined by $$\begin{aligned} \Vert \tau (P)\Vert _p:= \min _{F \in {\mathscr {P}}^l: P \not...
We denote by \(|A|:=\sum _{i,j} |A_{i,j}|\), if A is a square matrix. Note that \(W_\Gamma ({\textbf{k}})\) depends on \({\textbf{n}}\). Lemma 3.3 There exist \(C,\lambda _0>0\) independent of i such that for \(|\lambda |\le \lambda _0\), \(\widehat...