Related papers: A note on condition numbers for generalized invers…
The condition number of a linear function of the indefinite least squares solution is called the partial condition number for the indefinite least squares problem. In this paper, based on a new and very general condition number which can be…
In this paper, within a unified framework of the condition number theory we present the explicit expression of the projected condition number of the equality constrained indefinite least squares problem. By setting specific norms and…
An apriori bound for the condition number associated to each of the following problems is given: general linear equation solving, minimum squares, non-symmetric eigenvalue problems, solving univariate polynomials, solving systems of…
In this paper, we concentrate on the backward error and condition number of the indefinite least squares problem. For the normwise backward error of the indefinite least square problem, we adopt the linearization method to derive the tight…
In this paper, we consider the explicit expressions of the normwise condition number for the scaled total least squares problem. Some techniques are introduced to simplify the expression of the condition number, and some new results are…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…
In this paper, the normwise condition number of a linear function of the equality constrained linear least squares solution called the partial condition number is considered. Its expression and closed formulae are first presented when the…
Results on well-posedness of three inverse problems with integral conditions on a bounded interval for the generalized Korteweg-de Vries equation without any restrictions on the growth rate of nonlinearity are established. Either the…
In this paper, we consider the mixed and componentwise condition numbers for a linear function of the solution to the linear least squares problem with equality constrains (LSE). We derive the explicit expressions of the mixed and…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem…
The basic purpose of the present paper is the full solutions of the inverse problem (i.e. a finding of necessary and sufficient conditions) for the operator with complex periodic coefficients.
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
In this paper, we derive the mixed and componentwise condition numbers for a linear function of the solution to the total least squares with linear equality constraint (TLSE) problem. The explicit expressions of the mixed and componentwise…
Source conditions of the type $x^\dag \in\mathcal{R}((A^\ast A)^\mu)$ are an important tool in the theory of inverse problems to show convergence rates of regularized solutions as the noise in the data goes to zero. Unfortunately, it is…
In this paper, we present explicit expressions for the mixed and componentwise condition numbers of the truncated total least squares (TTLS) solution of $A\boldsymbol{x} \approx \boldsymbol{b} $ under the genericity condition, where $A$ is…
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…
In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…
In this paper, based on the theory of adjoint operators and dual norms, we define condition numbers for a linear solution function of the weighted linear least squares problem. The explicit expressions of the normwise and componentwise…