I n many of the numerical methods for pricing American options based on the dynamic programming approach, the most computationally intensive part can be formulated as the summation of Gaussians. Though this operation usually requires OONN work when there are N summations to compute and the number of terms appearing in each summation is N , we can reduce the… (More)
Based on the integrable discrete hungry Toda (dhToda) equation, the authors designed an algorithm for computing eigenvalues of a class of totally nonnegative matrices (Ann Mat Pura Appl, doi: 10.1007/s10231-011-0231-0 ). This is named the dhToda algorithm, and can be regarded as an extension of the well-known qd algorithm. The shifted dhToda algorithm has… (More)
In this article, we propose a new design method of ∆Σ modulators. We propose an optimal design to shape the frequency response of the noise transfer function (NTF). Generalized KYP (Kalman-Yakubovic-Popov) lemma is used to reduce our optimization to a linear matrix inequality. Design examples are illustrated to show effectiveness of our method.
The small-bulge multishift QR algorithm proposed by Bra-man, Byers and Mathias is one of the most eecient algorithms for computing the eigenvalues of nonsymmetric matrices on processors with hierarchical memory. However, to fully extract its po t e n tial performance, it is crucial to choose the block size m properly according to the target architecture and… (More)
In this paper, we give a causal solution to the problem of spline interpolation using H ∞ optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to reconstruct the inter-sample values. This leads to non-causality of the filter, and this becomes a critical issue for real-time… (More)