Related papers: Singular Values using Cholesky Decomposition
Originating in game theory, Shapley values are widely used for explaining a machine learning model's prediction by quantifying the contribution of each feature's value to the prediction. This requires a scalar prediction as in binary…
Under certain conditions, an element of a tensor product space can be identified with a compact operator and the singular value decomposition (SVD) applies to the latter. These conditions are not fulfilled in Sobolev spaces. In the previous…
We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
We present methods for computing the generalized polar decomposition of a matrix based on the dynamically weighted Halley (DWH) iteration. This method is well established for computing the standard polar decomposition. A stable…
Higher-order singular value decomposition (HOSVD) is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete…
Exploiting the explicit bijection between the density of singular values and the density of eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix size, we aim at finding the induced probability measure on…
In this note we use the divisorial Zariski decomposition to give a more intrinsic version of the algebraic Morse inequalities.
We consider the problem of recovering of initial data in the IBVP for the wave-type equation in the half-space by the solution restricted to the boundary. The singular value decomposition of this problem is concerned: the asymptotics of…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
In signal processing and identification, generalized singular value decomposition (GSVD), related to a sequence of matrices in product/quotient form are essential numerical linear algebra tools. On behalf of the growing demand for efficient…
In this paper, We use the Fourier series expansion of real variables function, We give a formula to calculate the Dirichlet character sum, and four special examples are given.
In this paper, we present a natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in nondegenerate real and complexified Clifford geometric algebras of arbitrary dimension and…
We describe how to compute topological objects associated to a polynomial map of several complex variables with isolated singularities. These objects are: the affine critical values, the affine Milnor numbers for all irregular fibers, the…
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the…
In this article we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using…
Welcome to a beautiful subject in scientific computing: numerical solution of ordinary differential equations (ODEs) with initial conditions.
Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.
We propose a tridiagonalization approach for non-Hermitian random matrices and Hamiltonians using singular value decomposition (SVD). This technique leverages the real and non-negative nature of singular values, bypassing the complex…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…