Numerical Computing
Numerical Computing - Related Videos
05:59
Numerical Cognition: More or Less
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2023
Source: Laboratories of Nicholaus Noles and Judith Danovitch—University of Louisville One of the goals of the modern education system is to teach children mathematical literacy. They are taught to add, subtract, multiply, and divide, and this base knowledge is used to support learning about geometry, algebra, calculus, physics, and statistics. School-aged children usually acquire these skills in formal educational settings, but the foundation of mathematical understanding is developed much...
01:24
Numerical Calculations
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2023
In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred. The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
01:21
Pilot and Numeric Relaying
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2024
Pilot relaying is a type of differential protection used in power systems. It compares electrical quantities at the terminals of equipment via a communication channel instead of direct relay interconnection. This method is essential for transmission lines where the terminals are far apart, typically up to 80 km for lines with 69 to 115 kV ratings. Four types of communication channels are used for pilot relaying: Pilot Wires: These are separate electrical circuits operating at DC, 50 to 60 Hz,...
00:59
How Data are Classified: Numerical Data
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2023
Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data are the result of counting or measuring the attributes of a population. Amount of money, pulse rate, weight, number of people living in a town, and number of students who opt for statistics are examples of quantitative data. Quantitative data may be either discrete or continuous. All quantitative data that take on only specific numerical...
12:39
Computational Fluid Dynamics Simulations of Blood Flow in a Cerebral Aneurysm
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2023
Source: Joseph C. Muskat, Vitaliy L. Rayz, and Craig J. Goergen, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana The objective of this video is to describe recent advancements of computational fluid dynamic (CFD) simulations based on patient- or animal-specific vasculature. Here, subject-based vessel segmentations were created, and, using a combination of open-source and commercial tools, a high-resolution numerical solution was determined within a flow model.
FAQs
Finite-precision arithmetic represents numbers with limited accuracy, so rounding can accumulate during calculations. The resulting error may remain negligible or become important when an algorithm is sensitive to small numerical changes. In statistical work, checking sensitivity to rounding and comparing results across computational settings helps identify whether estimates reflect the model or artifacts of unstable computation.
Regression calculations often require operations on matrices, especially when handling many observations or variables. Numerical linear algebra provides computationally practical ways to perform these operations without relying on exact symbolic solutions. Its effectiveness affects the accuracy, scalability, and reproducibility of regression results, making it a central component when statistical models must be evaluated on large datasets.
Maximum-likelihood estimation can require finding parameter values that optimize a model-dependent objective when an exact solution is unavailable. Numerical optimization approaches approximate this solution through successive calculations and must be evaluated for convergence. A result that has not converged reliably may not represent a meaningful estimate, so convergence checks are essential when interpreting fitted statistical models.
A stable method limits the effect of small changes in input values, rounding, or intermediate calculations on the final result. Sensitivity analysis helps reveal whether outputs change substantially under such perturbations, while convergence checks indicate whether an iterative calculation has reached a dependable result. Together, these evaluations help distinguish robust statistical conclusions from numerical artifacts.
A useful workflow begins by selecting an algorithm suited to the statistical calculation, then evaluating convergence and sensitivity rather than accepting an output automatically. Researchers should also examine whether results remain reproducible when the computation is repeated and whether numerical behavior is consistent with the model and data. These checks support more reliable interpretation of approximated estimates and probabilities.
Bayesian inference may require evaluating model quantities that are difficult to calculate exactly, particularly when the model or dataset is complex. Numerical methods provide approximate calculations that make these analyses computationally feasible. Their reliability depends on checking convergence and sensitivity, because an apparently precise posterior result can be misleading if the underlying computation has not stabilized.
Simulation provides a way to approximate probability-related results when direct calculation is impractical. By carrying out computational experiments, analysts can study model behavior and obtain numerical evidence for quantities that are difficult to evaluate exactly. The usefulness of those results depends on computational cost, reproducibility, and validation, especially when simulations support inference on large or complex datasets.