Yusaku Yamamoto

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In 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 O NN ′ work when there are N ′ summations to compute and the number of terms appearing in each summation is N , we can reduce(More)
This paper presents fast and accurate algorithms for computing the prices of discretely sampled lookback options. Under the Black-Scholes framework, the pricing of a discrete lookback option can be reduced to a series of convolutions of a function with the Gaussian distribution. Using this fact, an efficient algorithm, which computes these convolutions by a(More)
Designing communication-avoiding algorithms is crucial for high performance computing on a large-scale parallel system. The TSQR algorithm is a communication-avoiding algorithm for computing a tall-skinny QR factorization, and TSQR is known to be much faster and as stable as the classical Householder QR algorithm. The Cholesky QR algorithm is another very(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)
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 e cient algorithms for com puting the eigenvalues of nonsymmetric matrices on processors with hi erarchical memory However to fully extract its potential performance it is crucial to choose the block size m properly according to the target architecture and the(More)
Solution of large-scale dense nonsymmetric eigenvalue problem is required in many areas of scientific and engineering computing, such as vibration analysis of automobiles and analysis of electronic diffraction patterns. In this study, we focus on the Hessenberg reduction step and consider accelerating it in a hybrid CPU-GPU computing environment.(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)