This article points out that, with the now widespread availability of computers, the original χ2 statistic for testing goodness-of-fit no longer makes much sense. "χ2 and classical exact tests often wildly misreport significance; the remedy lies in computers," available in pdf, is a better place to start for the application-oriented.
This article can help accelerate interior-point methods for convex optimization, such as linear programming.
This article modifies and supplements tests of the Kolmogorov-Smirnov type (including Kuiper's).
This article simplifies the precomputations required for computing fast spherical harmonic transforms, complementing the approach taken in the article, "Fast algorithms for spherical harmonic expansions, II," available below.
This article is now out-of-date; instead, please see Nathan Halko's, Per-Gunnar Martinsson's, and Joel Tropp's SIAM Review paper.
This article provides a generally preferable alternative to the classical pivoted "QR" decomposition algorithms (such as Gram-Schmidt or Householder) for the low-rank approximation of arbitrary matrices. Constructing a low-rank approximation is the core step in computing several of the greatest singular values and corresponding singular vectors of a matrix.
This article provides an algorithm for linear least-squares regression. When the regression is highly overdetermined, the algorithm is more efficient than the classical methods based on "QR" decompositions.
This article provides efficient algorithms for computing spherical harmonic transforms, largely superseding our first article on the subject, "Fast algorithms for spherical harmonic expansions."
This article surveys algorithms for the compression of matrices.
This article provides details regarding the survey, "Randomized algorithms for the low-rank approximation of matrices," available above. "A randomized algorithm for the decomposition of matrices" is almost identical to our (better-known) technical report, "A randomized algorithm for the approximation of matrices," from 2006.
This article reviews the fact that numerically stable formulae exist for interpolating any linear combination of n bounded functions using the values of the linear combination at a certain collection of n points in the domain of the functions. The article also provides references to algorithms which determine these stable formulae at reasonably small computational expense.
This article is now largely (but not entirely) superseded by the paper, "Fast algorithms for spherical harmonic expansions, II," available above.