Skip to main content Accessibility help
×
  1. Home
  2. Browse subjects
  3. Mathematics
  4. Computational Science
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2540 results in Computational Science

Page 2 of 127

  • 1 - Tensors and Their Subparts

  • from Part I - Tensor Basics
  • Grey Ballard, Wake Forest University, North Carolina, Tamara G. Kolda, MathSci.ai
  • Book:
    Tensor Decompositions for Data Science
    Published online:
    05 June 2025
    Print publication:
    26 June 2025, pp 3-20
    • Chapter
      • You have access
    • PDF
    • Export citation

Tensor Decompositions for Data Science
  • Grey Ballard, Tamara G. Kolda
  • Published online:
    05 June 2025
    Print publication:
    26 June 2025
  • Tensors are essential in modern day computational and data sciences. This book explores the foundations of tensor decompositions, a data analysis methodology that is ubiquitous in machine learning, signal processing, chemometrics, neuroscience, quantum computing, financial analysis, social science, business market analysis, image processing, and much more. In this self-contained mathematical, algorithmic, and computational treatment of tensor decomposition, the book emphasizes examples using real-world downloadable open-source datasets to ground the abstract concepts. Methodologies for 3-way tensors (the simplest notation) are presented before generalizing to d-way tensors (the most general but complex notation), making the book accessible to advanced undergraduate and graduate students in mathematics, computer science, statistics, engineering, and physical and life sciences. Additionally, extensive background materials in linear algebra, optimization, probability, and statistics are included as appendices.

  • 2 - Brief Summary of Pseudospectral Methods

  • Bengt Fornberg, University of Colorado Boulder
  • Book:
    High-Accuracy Finite Difference Methods
    Published online:
    16 May 2025
    Print publication:
    05 June 2025, pp 17-25

  • Summary

    FD approximations of increasing orders of accuracy require correspondingly large stencil sizes. The limiting case of global stencils has numerous important applications, which have been extensively treated in the literature, under the acronym of pseudospectral (PS) methods. While the accuracy in certain cases can be very high, geometric flexibility typically becomes severely compromised. Our present summary aims mainly to provide some general insights into how PS methods relate to FD methods (rather than to describe PS implementation technicalities, such as, for nonperiodic problems, the necessity to cluster nodes very strongly toward the interval end points).

  • 3 - FD Approximations for Ordinary Differential Equations

  • Bengt Fornberg, University of Colorado Boulder
  • Book:
    High-Accuracy Finite Difference Methods
    Published online:
    16 May 2025
    Print publication:
    05 June 2025, pp 26-48

  • Summary

    The most common reason for approximating derivatives by finite differences is to apply these to solve ordinary and patrial differential equations – ODEs and PDEs, respectively. In the case of ODEs, many of the well-established (and seemingly quite different) procedures are immediately related to FD approximations – often more closely than may be apparent from how these methods are customarily described. Together with some basic convergence and stability theory, this chapter surveys a variety of ODE solvers, with emphasis on their FD connection and on the computational advantages that high-order accurate approximations can provide.

Page 2 of 127