Iterative refinement is a technique introduced by Wilkinson for reducing the roundoff error produced during the solution of simultaneous linear equations. Higher precision arithmetic is required for the calculation of the residuals.... 続きを読む >>

This is the third in a series of posts on the finite Fourier transform. The Fourier matrix produces an interesting graphic and has a surprising eigenvalue distribution. ... 続きを読む >>

For several years we thought Hadamard matrices showed maximum element growth for Gaussian elimination with complete pivoting. We were wrong. ... 続きを読む >>

In rare cases, Gaussian elimination with partial pivoting is unstable. But the situations are so unlikely that we continue to use the algorithm as the foundation for our matrix computations.... 続きを読む >>

The Singular Value Decomposition of the digram frequency matrix of a text coded with a simple substitution cypher can reveal information about the vowels and consonants in the text. ... 続きを読む >>

Employing a factorization based on the least significant singular values provides a matrix approximation with many surprisingly useful properties. This Reverse Singular Value Decomposition, RSVD, is also referred to as Subordinate Component Analysis, SCA, to distinguish it from Principal Component Analysis. ... 続きを読む >>

ContentsTim DavisSparse Matrix VisualizationsMusic VisualizationsMetastaseisBlue MondayElectrodoodleMorning Has BrokenBach Toccata and FugueNotesArt StudioTim DavisAt the recent SIAM conference on... 続きを読む >>

I am surprised when many of the singular values of a nonsymmetric variant of the Hilbert matrix turn out to be nearly equal to $\pi$. The explanation involves the Fourier series for a square wave.... 続きを読む >>

The Rosser matrix is a classic matrix eigenvalue test problem.... 続きを読む >>

The Fiedler companion matrix distributes the coefficients of a polynomial along the diagonals of an elegant pentadiagonal matrix whose eigenvalues are equal to the zeros of the polynomial.... 続きを読む >>