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ITC/USA 2007 Conference Proceedings / The Forty-Third Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2007 / Riviera Hotel & Convention Center, Las Vegas, Nevada / Robust adaptive beamforming using worst-case performance optimization is developed in recent years. It had good performance against array response errors, but it cannot reject strong interferences. In this paper, we propose a scheme for robust adaptive beamforming with broad nulls to reject strong interferences. We add a quadratic constraint to suppress the power of the array response over a spatial region of the interferences. The optimal weighting vector is then obtained by minimizing the power of the array output subject to quadratic constrains on the desired signal and interferences, respectively. We derive the formulations for the optimization problem and solve it efficiently using Newton recursive algorithm. Numerical examples are presented to compare the performances of the robust adaptive beamforming with no null constrains, sharp nulls and broad nulls. The results show its powerful ability to reject strong interferences.

Consider the D-optimal designs for a combined polynomial of degree d and trigonometric of order m regression on a partial circle [see Graybill (1976), p. 324]. It is shown that the structure of the optimal design depends only on the length of the design interval and that the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure.

The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.

This paper is concerned with the problem of computing theapproximate D-optimal design for polynomial regression with weight function w(x)>0 on the design interval I=[m_0-a,m_0+a]. It is shown that if w'(x)/w(x) is a rational function on I and a is close to zero, then the problem of constructing D-optimal designs can be transformed into a differential equation problem leading us to a certain matrix including a finite number of auxiliary unknown constants, which can be approximated by a Taylor expansion. We provide a recursive algorithm to compute Taylor expansion of these constants. Moreover, the D-optimal interior support points are the zeros of a polynomial which has coefficients that can be computed from a linear system.

This paper is concerned with the problem of constructing A-optimal design for polynomial regression with analytic weight function on the interval [m-a,m+a]. It is shown that the structure of the optimal design depends on a and weight function only, as a close to 0. Moreover, if the weight function is an analytic function a, then a scaled version of optimal support points and weights is analytic functions of a at $a=0$. We make use of a Taylor expansion which coefficients can be determined recursively, for calculating the A-optimal designs.

This paper is devoted to studying the problem of constructing Ds-optimal design for d-th degree polynomial regression with analytic weight function on the interval [m-a,m+a],m,a in R. It is demonstrated that the structure of the optimal design depends on d, a and weight function only, as a close to 0. Moreover, the Taylor polynomials of the scaled versions of the optimal support points and weights can be computed via a recursive formula.

Rigid multibody systems have been studied extensivley due to its direct application in design and analysis of various mechanical systems such as robots and spacecraft structures. The dynamics of multibody system is governed by its equations of motion and various terms associated with it, such as the mass matrix, the generalized force vector, are well known..Forward dynamics algorithms play an important role in the simulation of multibody systems and the recursive forward dynamics algorithm for branched multibody systems is very popular. The recursive forward dynamic algorithm is highly efficient algorithm with O(n) computational complexity and scores over other algorithms when number of rigid bodies n in the system is very large. The algorithm involves finding an important mass matrix, which has been popularly termed as articulated body inertia (AB inertia). To find ijth term of any general mass matrix, we separately give virtual change to ith and jth generalized coordinates. At each point of the multibody system, the dot product of the resulting virtual displacements are taken with each other and eventually integrated over the entire multibody system, weighted by the mass. This quantity divided by the virtual changes in ith and jth coordinates gives the ijth element of the mass matrix. This is one of the fundamental ways of looking at the mass matrix. However, in literature, the AB inertia is obtained as a result of mathematical manipulation and its physical or geometrical significance from the above view point is not clear. In this thesis we present a more geometric and physical explanation for the AB inertia. The main step is to obtain a new set of generalized coordinates which relate directly to the AB inertia. We have also shown the equivalence of our method with existing methods. A comprehensive treatement on change of generalized coordinates and its effect on equations of motion has also been presented as preliminaries. The second part of the thesis deals with closed loop multibody systems.A few years ago an iterative algorithm called the sequential regularization method (SRM) was proposed for simulation of closed loop multibody systems with attractive claims on its efficiency. In literature we find that this algorithm has been implemented and studied only for planar multibody systems. As a part of the thesis work, we have developed a C-programming language code which can simulate 3-dimensional spatial multibody systems using the SRM algorithm. The programme can also perform simulation using a relatively efficient Conventional algorithm having O(n+m3) complexity, where m denotes number of closed loop constraints. Simulation studies have been carried out on a few multibody systems using the two algorithms. Some of the results have been also been validated using the commercial simulation package -ADAMS. As a result of our simulation studies, we have detected certain points, after which the solution from SRM loses it convergence. More study is required to understand this lack of convergence.

This paper proposes a safety stock calculation function based on their distribution properties and create a guideline for the stock status optimization problem. The motivation for this paper originates the cooperation with a drilling tools company, Epiroc Drilling tools AB. The safety stock calculation divides all items into three distribution and design the safety stock for each types separately considering the influence of service level value and lead time. During the process of guideline design, complicated production chain framework is taken into account through recursive algorithm. The stock status combination which can give the minimum storage cost is the optimal guideline for stock item and non-stock item. The time for approximating the global minimum through exhaustive search is remarkably reduced due to the application of Parallel programming and statistical model.

<p>This thesis deals with the development of efficient and reliable algorithms and library software for factorizing matrices and solving matrix equations on high-performance computer systems. The architectures of today's computers consist of multiple processors, each with multiple functional units. The memory systems are hierarchical with several levels, each having different speed and size. The practical peak performance of a system is reached only by considering all of these characteristics. One portable method for achieving good system utilization is to express a linear algebra problem in terms of level 3 BLAS (Basic Linear Algebra Subprogram) transformations. The most important operation is GEMM (GEneral Matrix Multiply), which typically defines the practical peak performance of a computer system. There are efficient GEMM implementations available for almost any platform, thus an algorithm using this operation is highly portable.</p><p>The dissertation focuses on how recursion can be applied to solve linear algebra problems. Recursive linear algebra algorithms have the potential to automatically match the size of subproblems to the different memory hierarchies, leading to much better utilization of the memory system. Furthermore, recursive algorithms expose level 3 BLAS operations, and reveal task parallelism. The first paper handles the Cholesky factorization for matrices stored in packed format. Our algorithm uses a recursive packed matrix data layout that enables the use of high-performance matrix--matrix multiplication, in contrast to the standard packed format. The resulting library routine requires half the memory of full storage, yet the performance is better than for full storage routines.</p><p>Paper two and tree introduce recursive blocked algorithms for solving triangular Sylvester-type matrix equations. For these problems, recursion together with superscalar kernels produce new algorithms that give 10-fold speedups compared to existing routines in the SLICOT and LAPACK libraries. We show that our recursive algorithms also have a significant impact on the execution time of solving unreduced problems and when used in condition estimation. By recursively splitting several problem dimensions simultaneously, parallel algorithms for shared memory systems are obtained. The fourth paper introduces a library---RECSY---consisting of a set of routines implemented in Fortran 90 using the ideas presented in paper two and three. Using performance monitoring tools, the last paper evaluates the possible gain in using different matrix blocking layouts and the impact of superscalar kernels in the RECSY library. </p>