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In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…
Low-rank matrix recovery problems arise naturally as mathematical formulations of various inverse problems, such as matrix completion, blind deconvolution, and phase retrieval. Over the last two decades, a number of works have rigorously…
In recent years, deep learning has led to impressive results in many fields. In this paper, we introduce a multi-scale artificial neural network for high-dimensional non-linear maps based on the idea of hierarchical nested bases in the fast…
Sparse storage formats are techniques for storing and processing the sparse matrix data efficiently. The performance of these storage formats depend upon the distribution of non-zeros, within the matrix in different dimensions. In order to…
This work develops a fast, memory-efficient, and general algorithm for accelerated/undersampled dynamic MRI by assuming an approximate LR model on the matrix formed by the vectorized images of the sequence. By general, we mean that our…
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
We propose a robust normal estimation method for both point clouds and meshes using a low rank matrix approximation algorithm. First, we compute a local feature descriptor for each point and find similar, non-local neighbors that we…
Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs was considered in [9]. In this paper we present an improved algorithm for locating and continuing connecting orbits, which includes a…