Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

288
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
288
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

1.1K
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
1.1K
Newton’s Method01:30

Newton’s Method

11
Newton’s Method is a powerful iterative technique for approximating the roots of real-valued, differentiable functions, particularly when analytical solutions are impractical. This approach is widely used in scientific computing, engineering, and finance, where equations may be too complex for traditional algebraic methods to handle. The method relies on an iterative process that refines an initial estimate using the function’s derivative to approach the true solution progressively.
11
Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

161
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
161
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

18.8K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
18.8K
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

4.6K
The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...
4.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Optimizing viable bacteria detection in ballast tank sediments: Addressing PCR inhibitors and relic DNA.

Ecotoxicology and environmental safety·2025
Same author

A simple, randomized algorithm for diagonalizing normal matrices.

Calcolo·2025
Same author

Consecutive Steps of Membrane Insertion of the Two-spanning MscL Protein by Insertase YidC.

Journal of molecular biology·2025
Same author

Relic DNA obscures bacterial diversity and interactions in ballast tank sediment.

Environmental research·2024
Same author

Environmental RNA metabarcoding for ballast water microbial diversity: Minimizing false positives.

The Science of the total environment·2024
Same author

Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils.

BIT. Numerical mathematics·2024
Same journal

Column reduced digital nets.

Numerical algorithms·2026
Same journal

Vem++, a C++ library to handle and play with the virtual element method.

Numerical algorithms·2026
Same journal

The detection and correction of silent errors in pipelined Krylov subspace methods.

Numerical algorithms·2026
Same journal

Optimized Schwarz waveform relaxation methods for wave-heat coupling in one dimensional bounded domains.

Numerical algorithms·2025
Same journal

Patch area and uniform sampling on the surface of any ellipsoid.

Numerical algorithms·2025
Same journal

VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D.

Numerical algorithms·2025
See all related articles
  1. Home
  3. Randomized Methods For Computing Joint Eigenvalues, With Applications To Multiparameter Eigenvalue Problems And Root Finding.
  1. Home
  3. Randomized Methods For Computing Joint Eigenvalues, With Applications To Multiparameter Eigenvalue Problems And Root Finding.

Related Experiment Video

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

4.8K

Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root

Haoze He1, Daniel Kressner1, Bor Plestenjak2,3

  • 1École Polytechnique Fédérale de Lausanne (EPFL), Institute of Mathematics, 1015 Lausanne, Switzerland.

Numerical Algorithms
|October 14, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a novel randomized method for accurately approximating joint eigenvalues of commuting matrices. This approach enhances the performance of solvers for multiparameter eigenvalue problems and polynomial systems.

Keywords:
Commuting matricesJoint eigenvalueMultiparameter eigenvalue problemPolynomial systemRandomized numerical linear algebraRayleigh quotient

More Related Videos

Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria
08:33

Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria

Published on: July 28, 2023

955
Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

16.1K

Related Experiment Videos

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

4.8K
Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria
08:33

Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria

Published on: July 28, 2023

955
Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

16.1K

Area of Science:

  • Numerical Analysis
  • Linear Algebra
  • Computational Mathematics

Background:

  • Commuting matrix families are unitarily triangularizable, with diagonal entries representing joint eigenvalues.
  • Computing these joint eigenvalues is crucial for applications like multiparameter eigenvalue problems and solving multivariate polynomial systems.

Purpose of the Study:

  • To develop and analyze a numerical method for approximating joint eigenvalues of (nearly) commuting matrix families.
  • To demonstrate the effectiveness of the proposed method in improving existing solvers.

Main Methods:

  • Proposing a randomized approach that computes eigenvalues using Rayleigh quotients.
  • Utilizing eigenvectors from a random linear combination of matrices in the family.

Main Results:

  • The randomized method accurately computes semisimple joint eigenvalues.
  • Numerical examples demonstrate improved performance in relevant solvers.

Conclusions:

  • Randomized Rayleigh quotient methods offer an effective strategy for approximating joint eigenvalues.
  • This approach provides a valuable tool for tackling complex eigenvalue problems and polynomial systems.