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A Note On the Accuracy of Ramanujan's Approximative Formula for the Perimeter of an Ellipse
Ramanujan's approximative formula Best constants Elliptic functions and integrals
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2008/7/3
We present a detailed error analysis, with best possible constants, of Ramanujan's most accurate approximation to the perimeter of an ellipse.
Lattice Structure for Paraunitary Linear-Phase Filter Babks with Accuracy
Paraunitary Linear-phase Accuracy
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2007/12/12
Multivariate filter banks with a polyphase matrix built by matrix factorization (lattice structure) were proposed to obtain orthonormal wavelet basis. On the basis of that, we propose a general method...
High-Accuracy P-Stable Methods with MinimalPhase-Lag for $y''=f(t,y)$
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2007/12/12
In this paper, we develop a one-parameter family of P-stable
sixth-order and eighth-order two-step methods with minimal phase-lag
errors for numerical integration of second order periodic initial va...
Coverage Accuracy of Confidence Intervals in Nonparametric Regression
confidence interval empirical likelihood
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2007/12/11
Point-wise confidence intervals for a nonparametric regression function with random design points are considered. The confidence intervals are those based on the traditional normal approximation and t...
HIGH ACCURACY ANALYSIS OF ELLIPTIC EIGENVALUE PROBLEM FOR THE WILSON NONCONFORMING FINITE ELEMENT
Eigenvalue problems high accu
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2007/12/10
In this paper, the Wilson nonconforming finite element is considered for solving elliptic eigenvalue problems. Based on an interpolation postprocessing, superconvergence estimates of both eigenfuncti...