Posts 241 - 250 of 306

Periodic Solutions to the Lorenz Equations

Changing the value of a parameter in the equations that produce the famous Lorenz chaotic attractor yields nonlinear ordinary differential equations that have periodic solutions. ... read more >>

Singular Value Analysis of Cryptograms

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. ... read more >>

Reverse Singular Value Decomposition 2

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. ... read more >>

Higher Resolution Penny

High resolution measurements of the depth of the mold for the United States one cent coin provide an interesting data set.... read more >>

Music, Sparse Matrices, and London Billboards 2

ContentsTim DavisSparse Matrix VisualizationsMusic VisualizationsMetastaseisBlue MondayElectrodoodleMorning Has BrokenBach Toccata and FugueNotesArt StudioTim DavisAt the recent SIAM conference on... read more >>

The Tektronix 4081 2

The Tektronix 4081 minicomputer at Argonne National Laboratory in the summers of 1977 and '78 played an important role in the early development of MATLAB.... read more >>

Surprising SVD, Square Waves, and Pi 2

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.... read more >>

Magic Stars

Magic Stars are a little like Magic Squares. My grandson was introduced to them in his junior high school math class.... read more >>

The Rosser Matrix

The Rosser matrix is a classic matrix eigenvalue test problem.... read more >>

Fiedler Companion Matrix

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.... read more >>

Posts 241 - 250 of 306

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