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- John P. Boyd
- 2000

A computation is a temptation that should be resisted as long as possible. "

- John P. Boyd
- 1999

We introduce a new filter or sum acceleration method which is the complementary error function with a logarithmic argument. It was inspired by the large order asymptotics of the Euler and Vandeven accelerations, which we show are both proportional to the erfc function also. We also show the relationship between Vandeven’s filter, the Erfc-Log filter and the… (More)

- John P. Boyd, Jun Rong Ong
- 2008

Approximating a function from its values f (xi) at a set of evenly spaced points xi through (N+1)-point polynomial interpolation often fails because of divergence near the endpoints, the “Runge Phenomenon”. Here we briefly describe seven strategies, each employing a single polynomial over the entire interval, to wholly or partially defeat the Runge… (More)

- John P. Boyd
- 2004

To defeat Gibbs phenomenon in Fourier and Chebyshev series, Gottlieb et al. [D. Gottlieb, C.-W. Shu, A. Solomonoff, H. Vandeven, On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function, J. Comput. Appl. Math. 43 (1992) 81–98] developed a ‘‘Gegenbauer reconstruction’’. The partial sums of the… (More)

- John P. Boyd, William J. Fitzgerald, Robert J. Beck
- Social Networks
- 2006

The core/periphery structure is ubiquitous in network studies. The discrete version of the concept is that individuals in a group belong to either the core, which has a high density of ties, or to the periphery, which has a low density of ties. The density of ties between the core and the periphery may be either high or low. If the core/periphery structure… (More)

- John P. Boyd
- SIAM J. Numerical Analysis
- 2002

Robust polynomial rootfinders can be exploited to compute the roots on a real interval of a nonpolynomial function f(x) by the following: (i) expand f as a Chebyshev polynomial series, (ii) convert to a polynomial in ordinary, series-of-powers form, and (iii) apply the polynomial rootfinder. (Complex-valued roots and real roots outside the target interval… (More)

- John P. Boyd
- 2004

Bratu's problem, which is the nonlinear eigenvalue equation Au + 2 exp(u)= 0 with u = 0 on the walls of the unit square and 2 as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance of symmett:v: because of invariance under the C 4 rotation group and parity in both x and y, one… (More)

- John P. Boyd
- Applied Mathematics and Computation
- 2003

We introduce two methods for simultaneously approximating both branches of a two-branched function using Chebyshev polynomials. Both schemes remove the pernicious, convergence-wrecking effects of the square root singularity at the limit point where the two branches meet. The ‘‘Chebyshev–Shafer’’ method gives the approximants as the solution to a quadratic… (More)

- John P. Boyd
- 2003

By using complex variable methods (steepest descent and residues) to asymptotically evaluate the coefftcient integrals, the numerical analysis of Hermite function series is discussed. There are striking similarities and differences with the author’s earlier work on Chebyshev polynomial methods (J. Comp. Phys. 45 (1982), 45-49) for infinite or semi-infinite… (More)

- John P. Boyd, Martin G. Everett
- Social Networks
- 1999