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Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a collection of ...

With the advent of massive data sets, much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, ...

We develop and study incremental algorithms for truncated higher-order singular value decompositions. By combining the SVD updating and different truncated higher-order singular value decompositions, two incremental algorithms are proposed. Not ...

This paper focuses on algorithms for the truncated Takagi factorization of complex symmetric matrices. The problem is formulated as a Riemannian optimization problem on a complex Stiefel manifold and then is converted into a real Riemannian ...

In this paper, we develop a new technique to obtain improved estimates for the computational resolution limits in two-dimensional super-resolution problems and present a new idea for developing two-dimensional super-resolution algorithms. To be ...

The Trust Region Subproblem is a fundamental optimization problem that takes a pivotal role in Trust Region Methods. However, the problem, and variants of it, also arise in quite a few other applications. In this article, we present a family of ...

The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product-based third-order tensor singular value decomposition with the transformation matrix being a factor matrix of the higher-order ...

A High-Order Generalized Singular Value Decomposition (HO-GSVD) is employed to compare multiple matrices ${\{{\mathbf{A}}_i\}}_{i=1}^N$ with different row dimensions by using their generalized singular values ${\{{\sigma }_{i,k}\}}_{i=1}^N$ respectively. The ratio values of ${\sigma }_{i,k}/{\sigma }_{j,k}$ can ...${{\mathbf{}}_{}}_{\mathrm{}}^{}$${}_{}{}_{}$${\mathbf{}}_{\mathrm{}}{\mathbf{}}_{}$

In this work, we consider symmetric positive definite pencils depending on two parameters. That is, we are concerned with the generalized eigenvalue problem $\left(A(x)-\lambda B(x)\right)v=0$, where A and B are symmetric matrix valued functions in ${\mathbb{ℝ}}^{n\times n}$, smoothly ...$\mathrm{}{\mathbb{}}^{\mathrm{}}$

Computing spectra is a central problem in computational mathematics with an abundance of applications throughout the sciences. However, in many applications gaining an approximation of the spectrum is not enough. Often it is vital to determine ...

For a general third-order tensor $\mathcal{A}\in {\mathbb{R}}^{n\times n\times n}$ the paper studies two closely related problems, an SVD-like tensor decomposition and an (approximate) tensor diagonalization. We develop a Jacobi-type algorithm that works on $2\times 2\times 2$ subtensors and, in each ...

As a special UTV decomposition, the QLP decomposition is an effective alternative of the singular value decomposition (SVD) for the low-rank approximation. In this paper, we propose a single-pass randomized QLP decomposition algorithm for ...

Anymatrix is a MATLAB toolbox that provides an extensible collection of matrices with the ability to search the collection by matrix properties. Each matrix is implemented as a MATLAB function and the matrices are arranged in groups. Compared with ...

The quadratic matrix equation C ∗ X ∗ A X C + C ∗ X ∗ B + B ∗ X C + D = 0 , where A ∈ ℂ n × n , B ∈ ℂ n × p , C ∈ ℂ m × p and D ∈ ℂ p × p are given complex matrices with A ≥ 0 and D ∗ = D, and X ∈ ℂ n × m is a variable matrix to be determined, ...

For general complex or real 1-parameter matrix flows A(t)_{n, n} and for static matrices $A\in {\mathbb{ℂ}}_{n,n}$ alike, this paper considers ways to decompose matrix flows and single matrices globally via one constant matrix similarity C_{n, n} as A(t) = C^− 1 ⋅ diag(A₁(...

In this work, we consider the Takagi factorization of a matrix valued function depending on parameters. We give smoothness and genericity results and pay particular attention to the concerns caused by having either a singular value equal to 0 or multiple ...

The conjugate gradient method (CG) has long been the workhorse for inner-iterations of second-order algorithms for large-scale nonconvex optimization. Prominent examples include line-search based algorithms, e.g., Newton-CG, and those based on a trust-...

Approximate computing techniques, which trade off the computation accuracy of an algorithm for better performance and energy efficiency, have been successful in reducing computation and power costs in several domains. However, error sensitive ...

There are several factorizations of multidimensional tensors into lower-dimensional components, known as “tensor networks.” We consider the popular “tensor-train” (TT) format and ask, How efficiently can we compute a low-rank approximation from a full ...

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways ...