Results 61 to 70 of about 1,655,330 (212)

On a Discrete Inverse Problem for Two Spectra

Discrete Dynamics in Nature and Society, 2012
A version of the inverse spectral problem for two spectra of finite-order real Jacobi matrices (tridiagonal symmetric matrices) is investigated. The problem is to reconstruct the matrix using two sets of eigenvalues: one for the original Jacobi matrix ...
Gusein Sh. Guseinov
doaj   +1 more source

Rheological Modeling and Numerical Simulation of Annular Flow of a Drilling Mud Based on Local Materials: Theoretical Parametric Study

Engineering Reports, Volume 8, Issue 8, August 2026.
Numerical and analytical modeling of annular flow reveals the hydraulic performance of sustainable drilling muds formulated from Congolese kaolinitic clay, okra mucilage, and plant ashes. Yield stress enhances cuttings transport, while shear‐thinning behavior reduces pressure losses and pumping energy.
Stanislas Ulrich Berry Moukila
wiley   +1 more source

Analytic Results for the Eigenvalues of Certain Tridiagonal Matrices [PDF]

, 2008
The eigenvalue problem for a certain tridiagonal matrix with complex coefficients is considered. The eigenvalues and eigenvectors are shown to be expressible in terms of solutions of a certain scalar trigonometric equation.
Willms, Allan R.
core   +1 more source

Nordgren PINNs to VQE: Advancing Hydraulic Fracturing Simulations in Shale Reservoirs

International Journal for Numerical and Analytical Methods in Geomechanics, Volume 50, Issue 12, Page 4863-4878, 25 August 2026.
ABSTRACT This study advances hydraulic fracturing simulations in shale reservoirs using two computational paradigms, Physics‐Informed Neural Networks (PINNs) and the Variational Quantum Eigensolver (VQE). PINNs were employed to solve Nordgren's equation, which governs fracture width evolution, by embedding physical laws into the neural network ...
Dennis Delali Kwesi Wayo, Sonny Irawan, Mohd Zulkifli Bin Mohamad Noor, Mudasar Zafar, Shynar Juziyeva, Camila Martins Saporetti, Leonardo Goliatt, Randy Hazlett   +7 more
wiley   +1 more source

A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers

Mathematics, 2019
In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit ...
Yunlan Wei, Yanpeng Zheng, Zhaolin Jiang, Sugoog Shon   +3 more
doaj   +1 more source

Detecting When One Probe Vector is Enough for Preconditioned Log‐Determinant Approximation

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT We present randomized algorithms for estimating the log‐determinant of regularized symmetric positive semi‐definite matrices. The algorithms access the matrix only through matrix vector products, and are based on the introduction of a preconditioner and stochastic trace estimator.
Alice Cortinovis, Daniele Toni
wiley   +1 more source

Spectral Analysis of Block Diagonally Preconditioned Multiple Saddle‐Point Matrices With Inexact Schur Complements

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT We derive eigenvalue bounds for symmetric block‐tridiagonal multiple saddle‐point systems preconditioned with block‐diagonal Schur complement matrices. This analysis applies to an arbitrary number of blocks and accounts for the case where the Schur complements are approximated, generalizing the findings in [11, Bergamaschi et al., Linear ...
Marco Pilotto, Luca Bergamaschi, Ángeles Martínez   +2 more
wiley   +1 more source

Complexities of special matrix multiplication problems [PDF]

, 2018
This paper develops optimal algorithms to multiply an n × n symmetric tridiagonal matrix by: (i) an arbitrary n × m matrix using 2nm − m multiplications; (ii) a symmetric tridiagonal matrix using 6n − 7 multiplications; and (iii) a tridiagonal matrix ...
Takche, J.
core   +2 more sources

Lanczos algorithm explained in statistics

Results in Applied Mathematics
The Lanczos algorithm is a well-known three-term recurrence that can be used to generate an orthogonal basis for a Krylov subspace derived by a symmetric matrix.
Qiang Niu, Mianmian Chen, Jinheng Wu
doaj   +1 more source

The Use of Restarted Krylov Methods for Large Sparse Least Squares Problems

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT The use of restarted Krylov methods for solving large sparse linear least squares problems suffers from certain inherited difficulties. One of them arises in ill‐conditioned problems, when part of the residual vector is spanned by singular vectors that correspond to small singular values.
Achiya Dax
wiley   +1 more source