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

Emission Spectra02:39

Emission Spectra

75.8K
When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a range of energies, and thereby produce a continuous spectrum in which an unbroken series of wavelengths is present.
75.8K
Systematic Error: Methodological and Sampling Errors01:15

Systematic Error: Methodological and Sampling Errors

9.9K
In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...
9.9K
Fundamental Attribution Error01:14

Fundamental Attribution Error

13.7K
According to some social psychologists, people tend to overemphasize internal factors as explanations—or attributions—for the behavior of other people. They tend to assume that the behavior of another person is a trait of that person, and to underestimate the power of the situation on the behavior of others. They tend to fail to recognize when the behavior of another is due to situational variables, and thus to the person’s state. This erroneous assumption is...
13.7K
Random Error01:04

Random Error

9.1K
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
9.1K
Margin of Error01:27

Margin of Error

7.0K
The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
7.0K
Contaminants and Errors01:16

Contaminants and Errors

351
Effective sample preparation is crucial for accurate and reliable laboratory analysis. During this process, two significant sources of error can arise: concentration bias from improper sample splitting and contamination caused by methods used to reduce particle size, such as grinding or homogenization. Identifying and minimizing these potential errors is crucial to ensuring the validity of the analysis.
Another key consideration is determining the appropriate number of samples required to...
351

You might also read

Related Articles

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

Sort by
Same author

The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem.

Proceedings of the National Academy of Sciences of the United States of America·2022
Same author

A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics.

Proceedings. Mathematical, physical, and engineering sciences·2020
Same author

On instabilities of deep learning in image reconstruction and the potential costs of AI.

Proceedings of the National Academy of Sciences of the United States of America·2020
Same author

Compressed sensing MRI with variable density averaging (CS-VDA) outperforms full sampling at low SNR.

Physics in medicine and biology·2019
Same author

Correction to 'The unified transform for mixed boundary condition problems in unbounded domains'.

Proceedings. Mathematical, physical, and engineering sciences·2019
Same author

The unified transform for mixed boundary condition problems in unbounded domains.

Proceedings. Mathematical, physical, and engineering sciences·2019
Same journal

Erratum: Spectroscopy and Ground-State Transfer of Ultracold Bosonic ^{39}K^{133}Cs Molecules [Phys. Rev. Lett. 135, 203401 (2025)].

Physical review letters·2026
Same journal

Erratum: Lifetime of the ^{2}F_{7/2} Level in Yb^{+} for Spontaneous Emission of Electric Octupole Radiation [Phys. Rev. Lett. 127, 213001 (2021)].

Physical review letters·2026
Same journal

Laser-Plasma Based Seeded Free Electron Laser in the High-Gain Regime.

Physical review letters·2026
Same journal

Parent Hamiltonians for Stabilizer Quantum Many-Body Scars.

Physical review letters·2026
Same journal

Properties of Heavy Cosmic Nuclei Phosphorus, Chlorine, Argon, Potassium, and Calcium: Results from the Alpha Magnetic Spectrometer.

Physical review letters·2026
Same journal

Role of Spin-Isospin Symmetries in Nuclear β-Decays.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: Jan 21, 2026

Method for Recording Broadband High Resolution Emission Spectra of Laboratory Lightning Arcs
07:51

Method for Recording Broadband High Resolution Emission Spectra of Laboratory Lightning Arcs

Published on: August 27, 2019

7.3K

How to Compute Spectra with Error Control.

Matthew J Colbrook1, Bogdan Roman1, Anders C Hansen1

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

Physical Review Letters
|July 27, 2019
PubMed
Summary
This summary is machine-generated.

New algorithms reliably compute operator spectra, providing error bounds and approximate eigenvectors. These optimal methods are efficient, parallelizable, and solve previously intractable problems in computational science.

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.9K
Errors as a Means of Reducing Impulsive Food Choice
07:07

Errors as a Means of Reducing Impulsive Food Choice

Published on: June 5, 2016

9.1K

Related Experiment Videos

Last Updated: Jan 21, 2026

Method for Recording Broadband High Resolution Emission Spectra of Laboratory Lightning Arcs
07:51

Method for Recording Broadband High Resolution Emission Spectra of Laboratory Lightning Arcs

Published on: August 27, 2019

7.3K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.9K
Errors as a Means of Reducing Impulsive Food Choice
07:07

Errors as a Means of Reducing Impulsive Food Choice

Published on: June 5, 2016

9.1K

Area of Science:

  • Computational physics and chemistry
  • Quantum mechanics
  • Statistical mechanics

Background:

  • Computing operator spectra is crucial across scientific disciplines.
  • Existing algorithms lack guaranteed convergence, error bounds, or approximate eigenvectors, risking simulation inaccuracies.
  • The existence of reliable methods has been an open question since the 1950s.

Purpose of the Study:

  • To determine if universally reliable methods for computing operator spectra exist.
  • To develop algorithms that always converge, provide error bounds, and yield approximate eigenvectors.
  • To establish optimal computational approaches within the limits of digital computers.

Main Methods:

  • Development of novel algorithms for spectral computation.
  • Demonstration of algorithm optimality and efficiency.
  • Implementation and parallelization strategies for enhanced performance.

Main Results:

  • Affirmative resolution of the long-standing open problem regarding reliable spectral computation.
  • Algorithms guarantee convergence, provide error bounds, and compute approximate eigenvectors.
  • Demonstrated success on complex problems, including quasicrystal spectra and non-Hermitian phase transitions.

Conclusions:

  • Reliable and optimal algorithms for computing operator spectra are now available.
  • These methods significantly advance computational capabilities in physics, chemistry, and related fields.
  • The developed algorithms are practical, efficient, and extend the reach of scientific simulations.