Definition 1. An (archimedean) absolute value on a field k is a real valued function ‖ · ‖ : k → [0,∞) with the following three properties: (1) ‖x‖ = 0 if and only if x = 0. (2) ‖xy‖ = ‖x‖ · ‖y‖. (3) ‖x+ y‖ ≤ ‖x‖+ ‖y‖. A nonarchimedean absolute value satisfies the extra condition that (3’) ‖x+ y‖ ≤ max{‖x‖, ‖y‖}. If k is a field, we denote Mk the set of absolute values on k. As an abuse of nota...

This article introduces a bivariate shape-preserving interpolation algorithm to approximate the value function of a dynamic program. First, we present a savings allocation problem between a pension account and another non-pension one. With the objective of maximizing the present value of utility over a life cycle, the investor can distribute his or her savings, in each account, between stocks a...

Sequence Generator Projection Constraint Conjunction 1 scheme(612,34,18,34,1) id alldifferent*18 2 scheme(612,34,18,2,2) id alldifferent*153 3 scheme(612,34,18,1,18) id alldifferent*34 4 scheme(612,34,18,1,18) absolute value symmetric alldifferent([1..18])*34 5 scheme(612,34,18,17,1) absolute value alldifferent*36 6 repart(612,34,18,34,9) id sum ctr(0)*306 7 repart(612,34,18,34,9) id twin*1 8 r...

We calculate the storage modulus of a solution of semiiexible polymers in the plateau regime using a tube model that takes the eeect of nite polymer length into account. For experimentally relevant parameters the result shows the previously obtained scaling behavior. Our calculation allows a prediction for the absolute value of the modulus which is found to be in good agreement with recent rheo...

In this paper, we suggest and analyze an improved generalized Newton method for solving the NP-hard absolute value equations [Formula: see text] when the singular values of A exceed 1. We show that the global and local quadratic convergence of the proposed method. Numerical experiments show the efficiency of the method and the high accuracy of calculation.

Recently, two families of HSS-based iteration methods are constructed for solving the system of absolute value equations (AVEs), which is a class of non-differentiable NP-hard problems. In this study, we establish the Picard-CSCS iteration method and the nonlinear CSCS-like iteration method for AVEs involving the Toeplitz matrix. Then, we analyze the convergence of the Picard-CSCS iteration met...

This article advances our understanding of regression-based data mining by comparing the utility of Least Absolute Value (LAV) and Least Squares (LS) regression methods. Using demographic variables from U.S. state-wide data, we fit variable regression models to dependent variables of varying distributions using both LS and LAV. Forecasts generated from the resulting equations are used to compar...

Assume that the surplus of an insurer follows a compound Poisson surplus process. When the surplus is below zero or the insurer is on deficit, the insurer could borrow money at a debit interest rate to pay claims. Meanwhile, the insurer will repay debts from her premium income. The negative surplus may return to a positive level if debts are reasonable. However, when the negative surplus is bel...

We consider the problem of classifying completely or partially unlabeled data by using inequalities that contain absolute values of the data. This allows each data point to belong to either one of two classes by entering the inequality with a plus or minus value. By using such absolute value inequalities (AVIs) in linear and nonlinear support vector machines, unlabeled or partially labeled data...

We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the preconditioned minimal residual method with the inverse of the absolute value of the matrix as a preconditioner converges to the exact solution of the ...