The field of linear algebra and matrix factorization is moving towards the development of more efficient and robust algorithms for solving complex problems. Recent research has focused on improving the accuracy and scalability of methods for tensor decomposition, matrix approximation, and linear inverse problems. Innovations in techniques such as canonical decomposition, singular value decomposition, and perturbation analysis have led to significant advances in these areas. Furthermore, the development of new optimization algorithms and frameworks, such as variable projection and adaptive mixed precision, has expanded the range of problems that can be effectively solved. Notable papers in this area include those on the calculation of canonical decomposition via local discrepancies, constructive solutions to the common invariant cone problem, and perturbation analysis of singular values in concatenated matrices. Additionally, research on outlier-free isogeometric discretizations, priorconditioned sparsity-promoting projection methods, and unified perspectives on orthogonalization and diagonalization has also made significant contributions to the field.
Advances in Linear Algebra and Matrix Factorization
Sources
On calculation of canonical decomposition of Tensor via the grid of local discrepancies
Constructive solution of the common invariant cone problem
Perturbation Analysis of Singular Values in Concatenated Matrices
Outlier-free isogeometric discretizations for Laplace eigenvalue problems: closed-form eigenvalue and eigenvector expressions
Priorconditioned Sparsity-Promoting Projection Methods for Deterministic and Bayesian Linear Inverse Problems
A Unified Perspective on Orthogonalization and Diagonalization
$\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation
Geometric means of HPD GLT matrix-sequences: a maximal result beyond invertibility assumptions on the GLT symbols
Variable projection framework for the reduced-rank matrix approximation problem by weighted least-squares
A Double Inertial Forward-Backward Splitting Algorithm With Applications to Regression and Classification Problems
Tensor robust principal component analysis via the tensor nuclear over Frobenius norm
LHT: Statistically-Driven Oblique Decision Trees for Interpretable Classification
An Adaptive Mixed Precision and Dynamically Scaled Preconditioned Conjugate Gradient Algorithm
Consensus Seminorms and their Applications
Matrices over a Hilbert space and their low-rank approximation
Weighting operators for sparsity regularization
CART-ELC: Oblique Decision Tree Induction via Exhaustive Search