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

Linearization and Approximation01:26

Linearization and Approximation

45
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
45
Gain01:15

Gain

381
Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.
381
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

83
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
83
Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

1.1K
Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
1.1K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

360
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
360
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

357
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
357

You might also read

Related Articles

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

Sort by
Same author

Targeted next-generation sequencing reveals pathogen spectrum, drug resistance characteristics, and clinical determinants in children with community-acquired pneumonia.

Translational pediatrics·2026
Same author

Targeting CTSS Rescues LPS-Induced Osteogenic Impairment in PDLSCs via Blocking NF-κB-Dependent Inflammatory Responses.

Oral diseases·2026
Same author

Conveyor belt foreign object detection method based on improved YOLOv11 and ESRGAN.

Scientific reports·2026
Same author

A unified framework for air resistance coefficient identification and cruise control of high-speed trains.

ISA transactions·2026
Same author

The longitudinal and reversible causal link between depressive symptoms and cardiovascular disease among middle-aged and older adults: findings from three national cohorts.

Psychiatry research·2026
Same author

Compact simple dynamic holographic devices based on pattern-aligned liquid crystal micro-structures.

Applied optics·2026
Same journal

Hidden Data Recovery and Forecasting via Next-Generation Reservoir Computing With Multiscale Delay Selection.

IEEE transactions on neural networks and learning systems·2026
Same journal

CAFF-CIL: Causality-Aware Freedom Forgetting Approach for Class-Incremental Learning.

IEEE transactions on neural networks and learning systems·2026
Same journal

Harmonic Autoencoding Framework for Multiple Tasks in Magnetic Particle Imaging Reconstruction.

IEEE transactions on neural networks and learning systems·2026
Same journal

A Survey on Human-Centric Voice-Face Multimodal Learning.

IEEE transactions on neural networks and learning systems·2026
Same journal

Vision-Assisted Foundation Model for Solving Multitask Vehicle Routing Problems.

IEEE transactions on neural networks and learning systems·2026
Same journal

FP3O: Enabling Proximal Policy Optimization in Multiagent Cooperation With Parameter-Sharing Versatility.

IEEE transactions on neural networks and learning systems·2026
See all related articles

Related Experiment Video

Updated: Jan 22, 2026

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
06:22

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

Published on: August 28, 2019

5.5K

Multidimensional Gains for Stochastic Approximation.

Samer S Saab, Dong Shen

    IEEE Transactions on Neural Networks and Learning Systems
    |July 3, 2019
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces an iterative Jacobian-based method using a matrix gain for noisy root-finding problems. It enhances stability and convergence for vector-valued functions, aiding neural network training.

    More Related Videos

    Analysis of Multidimensional Microscopy Data Using Cell-ACDC
    06:17

    Analysis of Multidimensional Microscopy Data Using Cell-ACDC

    Published on: November 7, 2025

    518
    Databases to Efficiently Manage Medium Sized, Low Velocity, Multidimensional Data in Tissue Engineering
    09:43

    Databases to Efficiently Manage Medium Sized, Low Velocity, Multidimensional Data in Tissue Engineering

    Published on: November 22, 2019

    6.8K

    Related Experiment Videos

    Last Updated: Jan 22, 2026

    Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
    06:22

    Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

    Published on: August 28, 2019

    5.5K
    Analysis of Multidimensional Microscopy Data Using Cell-ACDC
    06:17

    Analysis of Multidimensional Microscopy Data Using Cell-ACDC

    Published on: November 7, 2025

    518
    Databases to Efficiently Manage Medium Sized, Low Velocity, Multidimensional Data in Tissue Engineering
    09:43

    Databases to Efficiently Manage Medium Sized, Low Velocity, Multidimensional Data in Tissue Engineering

    Published on: November 22, 2019

    6.8K

    Area of Science:

    • Numerical Analysis
    • Optimization Algorithms
    • Machine Learning

    Background:

    • Root-finding for vector-valued functions is challenging when evaluations are noisy.
    • Traditional methods often use scalar step sizes, which may not optimally handle multidimensional noisy data.

    Purpose of the Study:

    • To develop an iterative Jacobian-based recursion technique for noisy root-finding.
    • To introduce an iterate-dependent matrix gain to improve estimation accuracy.
    • To analyze algorithm stability and convergence properties for systems where M ≥ N.

    Main Methods:

    • Iterative Jacobian-based recursion with an iterate-dependent matrix gain.
    • Analytical development of the matrix gain based on noisy linear functions.
    • Proposing two algorithms: one for M ≥ N and another for M < N (underdetermined systems).

    Main Results:

    • Algorithms presented for both M ≥ N and M < N cases, assuming full Jacobian knowledge.
    • Demonstrated stability and convergence of the estimate error covariance matrix.
    • Convergence rate shown to be inversely proportional to the number of iterations for M ≥ N; guaranteed error covariance contraction for M < N.

    Conclusions:

    • The proposed algorithms effectively minimize mean square estimate error per iteration.
    • The technique provides a robust solution for root-finding with noisy data.
    • The underdetermined system approach is particularly applicable to training neural networks.