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

Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

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...
Synthetic Disvision of Polynomials01:28

Synthetic Disvision of Polynomials

Synthetic division is an efficient algorithmic approach for dividing a polynomial by a linear binomial of the form x - c, where c is a real number. This method is helpful due to its streamlined process, which avoids the more cumbersome steps involved in the traditional long division of polynomials. It simplifies computation and serves as a practical tool for evaluating polynomials and identifying their factors.To perform synthetic division, one begins by listing the coefficients of the...
Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

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...
Transformation of Plane Stress01:18

Transformation of Plane Stress

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

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 organic...
Angle of Twist: Problem Solving01:13

Angle of Twist: Problem Solving

An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the torque exerted...

You might also read

Related Articles

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

Sort by
Same author

Optimizing Absolute Binding Free Energy Calculations for Production Usage.

Journal of chemical theory and computation·2025
Same author

Basic Stability Tests of Machine Learning Potentials for Molecular Simulations in Computational Drug Discovery.

Journal of chemical information and modeling·2025
Same author

Evaluation of Machine Learning/Molecular Mechanics End-State Corrections with Mechanical Embedding to Calculate Relative Protein-Ligand Binding Free Energies.

Journal of chemical theory and computation·2025
Same author

Understanding the Catalytic Efficiency of Two Polyester Degrading Enzymes: An Experimental and Theoretical Investigation.

ACS omega·2024
Same author

On the Structure, Stability, and Cell Uptake of Nanostructured Lipid Carriers for Drug Delivery.

Molecular pharmaceutics·2024
Same author

Investigation of the Impact of Saccharides on the Relative Activity of Trypsin and Catalase after Droplet and Spray Drying.

Pharmaceutics·2023

Related Experiment Video

Updated: May 13, 2026

2D and 3D Matrices to Study Linear Invadosome Formation and Activity
12:25

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations.

Gerhard König1, Michael Moldaschl, Wilfried N Gansterer

  • 1University of Vienna, Department of Computational Biological Chemistry, Austria.

Journal of Computational and Applied Mathematics
|March 9, 2013
PubMed
Summary
This summary is machine-generated.

New algorithms for computing eigenvectors of symmetric block tridiagonal matrices offer significant speedups. These methods use twisted block factorizations to efficiently find eigenvectors, especially for large matrices.

Keywords:
Block tridiagonal matrixEigenvector computationInverse iterationTwisted block factorizationTwisted factorization

More Related Videos

Tracking the Mammary Architectural Features and Detecting Breast Cancer with Magnetic Resonance Diffusion Tensor Imaging
15:48

Tracking the Mammary Architectural Features and Detecting Breast Cancer with Magnetic Resonance Diffusion Tensor Imaging

Published on: December 15, 2014

Related Experiment Videos

Last Updated: May 13, 2026

2D and 3D Matrices to Study Linear Invadosome Formation and Activity
12:25

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

Tracking the Mammary Architectural Features and Detecting Breast Cancer with Magnetic Resonance Diffusion Tensor Imaging
15:48

Tracking the Mammary Architectural Features and Detecting Breast Cancer with Magnetic Resonance Diffusion Tensor Imaging

Published on: December 15, 2014

Area of Science:

  • Numerical Analysis
  • Linear Algebra
  • Scientific Computing

Background:

  • Computing eigenvectors of symmetric block tridiagonal matrices is crucial in various scientific and engineering fields.
  • Existing methods, often based on tridiagonalization, can be computationally intensive for large matrices.

Purpose of the Study:

  • To develop novel, efficient algorithms for computing eigenvectors of symmetric block tridiagonal matrices.
  • To leverage twisted block factorizations for improved computational performance.

Main Methods:

  • Exploration of new methods based on twisted block factorizations.
  • Review of the relationship between block factorizations and eigenvectors.
  • Design of algorithmic strategies utilizing inverse iteration with starting vectors derived from factorizations.

Main Results:

  • Proposed algorithms demonstrate substantial reductions in runtime compared to state-of-the-art methods, particularly for large matrices and small bandwidths.
  • Numerical accuracy, measured by residuals, is generally comparable to existing techniques.
  • A minor loss in eigenvector orthogonality was observed in specific cases with clustered eigenvalues.

Conclusions:

  • The novel algorithms based on twisted block factorizations provide an efficient approach for eigenvector computation.
  • Future research will focus on addressing the observed orthogonality issues in cases of clustered eigenvalues.