A new parallel symmetric successive over-relaxation (PSSOR) preconditioner is proposed in this paper by the multi-type partition techniques introduced in SIAM J. Scientific Computing 20, 2006, pp. 1513-1533. In a general matrix expression, it is proved to be symmetric and positive-definite if the coefficient matrix of a linear system is symmetric and positive-definite. It is also proved to be e...

This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston [18], and by a Poisson jump process of the type originally introduced by Merton [25]. We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, t...

We observe that in a simple one-dimensional polynomial optimization problem (POP), the ‘optimal’ values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation problems are strictly and significantly less than that value. Some pieces of circumstantial evidences for the st...

We develop a method of poroelastic relaxation indentation (PRI) to characterize thin layers of gels. The solution to the time-dependent boundary-value problem is obtained in a remarkably simple form, so that the force-relaxation curve obtained by indenting a gel readily determines all the poroelastic constants of the gel—the shear modulus, Poisson’s ratio, and the effective diffusivity. The met...

The modified integer round-up property (MIRUP) for a linear integer minimization problem means that the optimal value of this problem is not greater than the optimal value of the corresponding LP relaxation rounded up plus one. In earlier papers the MIRUP was shown to hold for the so-called divisible case and some other subproblems of the one-dimensional cutting stock problem. In this paper we ...

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inger equation (TDSE). It uses the Crank–Nicholson scheme to propthen solving the resulting eigenproblem by expanding on agate the wavefunction forward in time and finite differences to some basis set. Examples of such techniques are the colloapproximate the derivative operators. The resulting sparse linear cation and Galerkin methods implemented via piecewise system is solved by the symmetric ...