Search Results - "Borwein, P. B."

A complete description of Golay pairs for lengths up to 100 by Borwein, P. B., Ferguson, R. A.

“…In his 1961 paper, Marcel Golay showed how the search for pairs of binary sequences of length n with complementary autocorrelation is at worst a…”
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Monic integer Chebyshev problem by BORWEIN, P. B, PINNER, C. G, PRITSKER, I. E

“…We study the problem of minimizing the supremum norm by monic polynomials with integer coefficients. Let {\M}_n({\Z}) denote the monic polynomials of degree n…”
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A Cubic Counterpart of Jacobi's Identity and the AGM by Borwein, J. M., Borwein, P. B.

“…We produce exact cubic analogues of Jacobi's celebrated theta function identity and of the arithmetic-geometric mean iteration of Gauss and Legendre. The…”
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Some Cubic Modular Identities of Ramanujan by Borwein, J. M., Borwein, P. B., Garvan, F. G.

“…There is a beautiful cubic analogue of Jacobi's fundamental theta function identity: θ4 3= θ4 4+ θ4 2. It is (∑∞ n, m = -∞qn2+ nm + m2 )3= (∑∞ n, m = -∞ωn -…”
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On the Complexity of Familiar Functions and Numbers by Borwein, J. M., Borwein, P. B.

“…This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that it is possible to base a taxonomy of such…”
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Strange Series and High Precision Fraud by Borwein, J. M., Borwein, P. B.

“…Twelve series approximations in which five are exact and seven are not identities but are approximations that are correct to at least 30 digits are presented…”
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The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions by Borwein, J. M., Borwein, P. B.

“…We produce a self contained account of the relationship between the Gaussian arithmetic-geometric mean iteration and the fast computation of elementary…”
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A Cubic Counterpart of Jacobi's Identity and the AGM by Borwein, J. M., Borwein, P. B.

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Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi by Borwein, J. M., Borwein, P. B., Bailey, D. H.

“…One of Ramanujan's approaches to approximating pi is considered. As understanding of Ramanujan's work increases, the mathematics involved are demystified…”
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A very rapidly convergent product expansion for π by BORWEIN, J. M, BORWEIN, P. B

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Challenges in mathematical computing by Borwein, J.M., Borwein, P.B.

“…Almost all interesting mathematical algorithmic questions relate to NP-hard questions. Such computation is prone to explode exponentially. The authors…”
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The Multivariate Integer Chebyshev Problem by Borwein, P. B., Pritsker, I. E.

“…The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in ℂ d . We…”
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Giuga's Conjecture on Primality by Borwein, D., Borwein, J. M., Borwein, P. B., Girgensohn, R.

“…There are infinitely many Giuga sequences that mathematicians can formulate. It is demonstrated that it is possible to generate longer Giuga sequences out of…”
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Incomplete rational approximation in the complex plane by Borwein, P. B., Chen, Weiyu

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On the mean iteration (a,b) ← (a+3b/4, √ab+b/2) by BORWEIN, J. M, BORWEIN, P. B

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Giuga's Conjecture on Primality by Borwein, D., Borwein, J. M., Borwein, P. B., Girgensohn, R.

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A Polynomial Problem by Borwein, P. B.

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A Generalized Arithmetic-Geometric Mean by Borwein, D., Borwein, P. B.

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Pi, Euler Numbers, and Asymptotic Expansions by Borwein, J. M., Borwein, P. B., Dilcher, K.

“…A series for pi, truncated at 500,000 terms, gives to forty places. The sixth digit after the decimal point is wrong, but the next ten digits are correct. An…”
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More Quadratically Converging Algorithms for $\pi by Borwein, J. M., Borwein, P. B.

“…We present a quadratically converging algorithm for $\pi$ based on a formula of Legendre's for complete elliptic integrals of modulus $\sin(\pi/12)$ and the…”
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