Related papers: Perturbation analysis for the periodic generalized…
In this paper, we adopt a componentwise perturbation analysis for $\star$-Sylvester equations. Based on the small condition estimation (SCE), we devise the algorithms to estimate normwise, mixed and componentwise condition numbers for…
By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the linear componentwise perturbation bounds for unitary factors and upper triangular factors of the generalized Schur…
This paper is devoted to a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the analysis, the upper bounds for the structured normwise, mixed and componentwise…
A new closed formula for the first order perturbation estimate of the mixed least squares-total least squares (MTLS) solution is presented. It is mathematically equivalent to the one by Zheng and Yang(Numer. Linear Algebra Appl. 2019;…
The design and structure of generalized predictive control (GPC) are not simple and intuitive. The performance analysis does not deeply analyze how the controller parameters affect the system characteristics and the relationship between the…
Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always…
For real matrices of full column-rank, we analyze the conditioning of several types of normal equations that are preconditioned by a randomized preconditioner computed in lower precision. These include symmetrically preconditioned normal…
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…
Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate the…
In this paper, we consider the mixed and componentwise condition numbers for a linear function of the solution to the total least squares (TLS) problem. We derive the explicit expressions of the mixed and componentwise condition numbers…
We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive…
Both structured componentwise and structured normwise perturbation analysis of the Tikhonov regularization are presented. The structured matrices under consideration include: Toeplitz, Hankel, Vandermonde, and Cauchy matrices. Structured…
Numerical analysis is conducted for a generalized particle method for a Poisson equation. Unique solvability is derived for the discretized Poisson equation by introducing a connectivity condition for particle distributions. Moreover, by…
Consider the nonlinear matrix equation X-sum_{i=1}^{m}A_{i}^{*}X^{p_{i}}A_{i}=Q with p_{i}>0. Sufficient and necessary conditions for the existence of positive definite solutions to the equation with p_{i}>0 are derived. Two perturbation…
Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are…
In this paper we show a general Strichartz estimate for certain perturbed wave equation, and here we can drop the nontrapping hypothesis and handle trapping obstacles with some loss of derivatives for data in the local energy decay…
Perturbative Symmetry Approach is formulated in symbolic representation. Easily verifiable integrability conditions of a given equation are constructed in the frame of the approach. Generalisation for the case of non-local and non-evolution…
Generalized polynomial chaos expansions are a powerful tool to study differential equations with random coefficients, allowing in particular to efficiently approximate random invariant sets associated to such equations. In this work, we use…
Statistical inference for stochastic block models typically relies on the spectrum of the normalized adjacency matrix $\A^*$. In practice, the true probability matrix $\mathbf{B}$ is unknown and must be replaced by a plug-in estimator…
The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…