Based on the Legendre pseudospectral method, we propose a numerical treatment for pricing perpetual American put option with stochastic volatility. In this simple approach, a nonlinear algebraic equation system is first derived, and then solved by the Gauss-Newton algorithm. The convergence of the current scheme is ensured by constructing a test example similar to the original problem, and comp...

ITPACK 2C is a collection of seven FORTRAN subroutines for solving large sparse linear systems by adaptive accelerated iterative algorithms. Basic iterative procedures, such as the Jacobi method, the Successive Overrelaxation method, the Symmetric Successive Overrelaxation method, and the RS method for the reduced system are combined, where possible, with acceleration procedures such as Chebysh...

Introduction The goal is to find factors of a given number N with n bits as required for various purposes. This may be done in a quantum algorithm processor fabricated in CMOS as originally promoted by the author [1]. Each register may execute in parallel the instructions in a wiring diagram to accomplish division by integers from 2 to √N. This amounts to dividing by all n/2 bit divisors (for n...

A model of inductive inquiry is defined within the context of first-order logic. The model conceives of inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players, along with a partition of a class of countable structures for that vocabulary. Next, Nature secretly chooses one structure (“the real world”) from some cell of the p...

The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is...

For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves soluti...

We accelerate the time-consuming iterations for projective reconstruction, a key component of self-calibration for computing 3-D shapes from feature point tracking over a video sequence. We first summarize the algorithms of the primal and dual methods for projective reconstruction. Then, we replace the eigenvalue computation in each step by the power method. We also accelerate the power method ...

Deformed algebras (usually called ‘quantum groups’) have received great attention since the original works of Drinfel’d, Jimbo and Faddeev, Reshetikhin and Takhtajan [1, 2, 3, 4] which gave a (unique) deformation procedure for simple Lie algebras. However, the deformation of non-simple Lie algebras has been characterized by the lack of a definite prescription and this explains why inhomogeneous...

There is a current need for scheduling policies that can leverage the performance variability observed when scheduling parallel computations on multi-user clusters. We develop one solution to this problem called stochastic scheduling that utilizes a distribution of application execution performance on the target resources to determine a performance-efficient schedule. In this paper, we define a...

This paper considers a generalization of the classical red/black ordering of grid points for f ini te difference or f i n i t e element discret i z a t i o n s shown t o be effective i n the implementation of the SOR i terat ion method on vector or parallel computers. orderings for different discretizations and implementation on the CDC Cyber 203/205 and the Finite Element Machine i s discussed...