Related papers: A Riemannian Inexact Newton-CG Method for Nonnegat…
We extend the ultraspherical spectral method to solving nonlinear ODE boundary value problems. We propose to use the inexact Newton-GMRES framework for which an effective preconditioner can be constructed and a fast Jacobian-vector…
In this paper, we initiate the study of the inverse eigenvalue problem for probe graphs. A probe graph is a graph whose vertices are partitioned into probe vertices and non-probe vertices such that the non-probe vertices form an independent…
We study the bisymmetric nonnegative inverse eigenvalue problem (BNIEP). This problem is the problem of finding the necessary and sufficient conditions on a list of $n$ complex numbers to be a spectrum of an $n \times n$ bisymmetric…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…
We deal with the problem of description of nonsingular pairs of compatible flat metrics for the general $N$-component case. We describe the scheme of the integrating the nonlinear equations describing nonsingular pairs of compatible flat…
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…
We address an algorithm for the least squares fitting of a subset of the eigenvalues of an unknown Hermitian matrix lying an an affine subspace, called the Lift and Projection (LP) method, due to Chen and Chu (SIAM Journal on Numerical…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…
Let $A$ be a nonnegative symmetric $ 5 \times 5 $ matrix with eigenvalues $ \lambda_1 \geq \lambda_2 \geq \lambda_3 \geq \lambda_4 \geq \lambda_5 $. We show that if $ \sum_{i=1}^{5} \lambda_{i} \geq \frac{1}{2} \lambda_1 $ then $ \lambda_3…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear…
Let $G$ be an undirected graph on $n$ vertices and let $S(G)$ be the set of all $n \times n$ real symmetric matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of $G$. The inverse eigenvalue…
In this paper, inexact Gauss-Newton like methods for solving injective-overdetermined systems of equations are studied. We use a majorant condition, defined by a function whose derivative is not necessarily convex, to extend and improve…
We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…
The main aim of this paper is to solve an inverse source problem for a general nonlinear hyperbolic equation. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the…
The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$ complex numbers (counting multiplicity) occur as the eigenvalues of some $n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a known hard…
Motivated by a class of nonlinear imaging inverse problems, for instance, multispectral computed tomography (MSCT), this paper studies the convergence theory of the nonlinear Kaczmarz method (NKM) for solving the system of nonlinear…
Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such estimators for conjugate gradient algorithms used to solve…