Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

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
×

2 results

  • 2 - Bases and Similarity

  • Stephan Ramon Garcia, Pomona College, California, Roger A. Horn, University of Utah
  • Book:
    Matrix Mathematics
    Published online:
    29 September 2023
    Print publication:
    25 May 2023, pp 26-55

  • Summary

    Chapter 2: Linearly independent lists of vectors that span a vector space are of special importance. They provide a bridge between the abstract world of vector spaces and the concrete world of matrices. They permit us to define the dimension of a vector space and motivate the concept of matrix similarity.

  • 9 - Polynomial Interpolation

  • from Part II - Constructive Approximation Theory
  • Abner J. Salgado, University of Tennessee, Knoxville, Steven M. Wise, University of Tennessee, Knoxville
  • Book:
    Classical Numerical Analysis
    Published online:
    29 September 2022
    Print publication:
    20 October 2022, pp 231-265

  • Summary

    We study the problem of polynomial interpolation. Its solution with the Vandermonde matrix, and with a Lagrange nodal basis are then presented, and error estimates are provided. The Runge phenomenon is then illustrated. Hermite interpolation then is studied, its solution is given, and error estimates are provided. The problem of Lagrange interpolation is then generalized to the case of holomorphic functions on the complex plane, and error estimates are provided. A more efficient construction, via divided differences, is then given for the interpolating polynomial. We extend the notion of divided differences, in order to use them to provide error estimates for polynomial interpolation.