Results 21 to 30 of about 62,500 (93)

High relative accuracy with some special matrices related to Γ and β functions

Numerical Linear Algebra with Applications, Volume 30, Issue 5, October 2023., 2023
Abstract For some families of totally positive matrices using Γ$$ \Gamma $$ and β$$ \beta $$ functions, we provide their bidiagonal factorization. Moreover, when these functions are defined over integers, we prove that the bidiagonal factorization can be computed with high relative accuracy and so we can compute with high relative accuracy their ...
Jorge Delgado, Juan Manuel Peña
wiley   +1 more source

The power of bidiagonal matrices [PDF]

Bidiagonal matrices are widespread in numerical linear algebra, not least because of their use in the standard algorithm for computing the singular value decomposition and their appearance as LU factors of tridiagonal matrices.
Higham, Nicholas J.
core   +4 more sources

High Relative Accuracy for Corner Cutting Algorithms

Axioms
Corner cutting algorithms are important in computer-aided geometric design and they are associated to stochastic non-singular totally positive matrices. Non-singular totally positive matrices admit a bidiagonal decomposition. For many important examples,
Jorge Ballarín, Jorge Delgado, Juan Manuel Peña   +2 more
doaj   +1 more source

Positive bidiagonal factorization of tetradiagonal Hessenberg matrices

, 2022
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. In this paper conditions, in terms of continued fractions, for an oscillatory tetradiagonal Hessenberg matrix to
Mañas, Manuel, Foulquié-Moreno, Ana, Branquinho, Amílcar   +2 more
core  

Bidiagonal factoring of Stirling matrices

Maple Transactions
Stirling cycle numbers and Stirling partition numbers have many combinatorial applications. A symmetric matrix built from Stirling cycle numbers, which is known to be totally nonnegative, appears as https://oeis.org/A137854 in the Online Encyclopedia of Integer Sequences. In this paper we give analytical bidiagonal factorings of these matrices.
Robert M. Corless, David J. Jeffrey, Qingze Li   +2 more
openaire   +1 more source

Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices [PDF]

Bulletin of Mathematical Sciences and Applications, 2015
A non-unit bidiagonal matrix and its inverse with simple structures are introduced. These matrices can be constructed easily using the entries of a given non-zero vector without any computations among the entries. The matrix transforms the given vector to a column of the identity matrix. The given vector can be computed back without any round off error
openaire   +1 more source

Bidiagonal factorization of tetradiagonal matrices and Darboux transformations

, 2022
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory.
Mañas, Manuel, Foulquié-Moreno, Ana, Branquinho, Amílcar   +2 more
core  

Polynomial Preconditioning for Indefinite Matrices

Numerical Linear Algebra with Applications, Volume 33, Issue 5, October 2026.
ABSTRACT Polynomial preconditioning is an important tool in solving large linear systems and eigenvalue problems. A polynomial from GMRES can be used to precondition restarted GMRES and restarted Arnoldi. Here we give methods for indefinite matrices that make polynomial preconditioning more generally applicable. The new techniques include balancing the
Hayden Henson, Ronald B. Morgan
wiley   +1 more source

Directional clustering through matrix factorization [PDF]

, 2016
This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction.
Blumensath, Thomas
core   +1 more source

Bidiagonal Decompositions and High‐Accuracy Computations for Newton Collocation Matrices

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT We consider a class of collocation matrices A$$ A $$ associated with the Newton basis of the space of polynomials of degree at most n$$ n $$, evaluated at a set of l+1≥n+1$$ l+1\ge n+1 $$ nodes. In the most general setting, we allow n$$ n $$ of these nodes to either coincide with or differ from those defining the Newton basis.
E. Mainar, A. Marco, B. Rubio, R. Viaña
wiley   +1 more source