Search results for "Numerical linear algebra"
showing 3 items of 3 documents
An iterative method for pricing American options under jump-diffusion models
2011
We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou@?s and Merton@?s jump-diffusion models show that the resulting iteration converges rapidly.
High-quality computational tools for linear-algebra problems in FEM electromagnetic simulation [EM Programmer's Notebook]
2004
A key ingredient of finite-element analysis programs is the linear-algebra solver, typically either a linear-system solver or an eigensolver. The first part of This work tries to justify why it is important to have recourse to publicly available software for addressing this part of the computation. A number of libraries are mentioned as successful examples that exhibit a series of desirable qualities. Although some of these libraries force the programmer to somewhat change the programming style and may be difficult to learn, the benefits usually pay off the extra effort. The second part of the paper describes one of these libraries in some detail, namely SLEPc, the Scalable Library for Eige…
State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve.
2004
We study the nitrogen binding curve with the density matrix renormalization group (DMRG) and single-reference and multireference coupled cluster (CC) theory. Our DMRG calculations use up to 4000 states and our single-reference CC calculations include up to full connected hextuple excitations. Using the DMRG, we compute an all-electron benchmark nitrogen binding curve, at the polarized, valence double-zeta level (28 basis functions), with an estimated accuracy of 0.03mE_h. We also assess the performance of more approximate DMRG and CC theories across the nitrogen curve. We provide an analysis of the relative strengths and merits of the DMRG and CC theory under different correlation condition…