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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)

- Yusaku Yamamoto, Takeshi Fukaya, Takashi Uneyama, Masami Takata, Kinji Kimura, Masashi Iwasaki +1 other
- PaCT
- 2007

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 paper, we present a new approach to optimizing the blocking strategy for the householder QR decomposition. In high performance implementations of the householder QR algorithm, it is common to use a blocking technique for the efficient use of the cache memory. There are several well known blocking strategies like the fixed-size blocking and recursive… (More)

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)

The nonlinear eigenvalue problem plays an important role in various fields such as nonlinear elasticity, electronic structure calculation and theoretical fluid dynamics. We recently proposed a new algorithm for the nonlinear eigenvalue problem, which reduces the original problem to a smaller generalized linear eigenvalue problem with Hankel coefficient… (More)

Traces of inverse powers of a positive definite symmetric tridiagonal matrix give lower bounds of the minimal singular value of an upper bidiagonal matrix. In a preceding work, a formula for the traces which gives the diagonal entries of the inverse powers is presented. In this paper, we present another formula which gives the traces based on a quite… (More)