Solving nonlinear equations is a problem often needed to be dealt with in the practical engineering application. This paper discusses preconditioning methods based on Block Broyden method. It first introduces the Block Broyden method and preconditioning technique. Then it presents four different preconditioners for the Block Broyden method and discusses the implementation process. It also analy...

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...

Abstract: Training a SVR (support vector regression) requires the solution of a very large QP (quadratic programming) optimization problem. Despite the fact that this type of problem is well understood, the existing training algorithms are very complex and slow. In order to solve these problems, this paper firstly introduces a new way to make SVR have the similar mathematic form as that of a su...

This paper illustrates the current state of development of an algorithm for the steady state solution of continuous-time Markov chains. The so-called multi-level algorithm utilizes ideas from algebraic multigrid to provide an efficient alternative to the currently used Gauss-Seidel and successive overrelaxation methods. The multi-level method has been improved through several iterations, so tha...

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...

This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and Successive Over-Relaxation (GS/SOR) schemes. Our study is indeed based on the application of a preconditioned bi-conjugate gradient metho...