Recursive Matrix Calculation Paradigm by the Example of Structured Matrix

Jerzy S. Respondek

doi:10.3390/info11010042

Recursive Matrix Calculation Paradigm by the Example of Structured Matrix

Information ◽

10.3390/info11010042 ◽

2020 ◽

Vol 11 (1) ◽

pp. 42

Author(s):

Jerzy S. Respondek

Keyword(s):

Computational Complexity ◽

Programming Language ◽

Numerical Algorithm ◽

General Purpose ◽

Recursive Algorithms ◽

Structured Matrix ◽

Symbolic Calculations ◽

Recursive Matrix ◽

Matrix Calculation ◽

Better Than

In this paper, we derive recursive algorithms for calculating the determinant and inverse of the generalized Vandermonde matrix. The main advantage of the recursive algorithms is the fact that the computational complexity of the presented algorithm is better than calculating the determinant and the inverse by means of classical methods, developed for the general matrices. The results of this article do not require any symbolic calculations and, therefore, can be performed by a numerical algorithm implemented in a specialized (like Matlab or Mathematica) or general-purpose programming language (C, C++, Java, Pascal, Fortran, etc.).

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An Improved Method for CT Image Coding Using PSNR Prediction Model Based on ELM

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.738-739.598 ◽

2015 ◽

Vol 738-739 ◽

pp. 598-601

Author(s):

Han Yang Zhu ◽

Xin Yu Jin ◽

Jian Feng Shen

Keyword(s):

Computational Complexity ◽

Prediction Model ◽

Image Coding ◽

Region Of Interest ◽

Image Encoding ◽

Large Size ◽

Learning Machine ◽

Intractable Problem ◽

Encoding Efficiency ◽

Better Than

In telemedicine, medical images are always considered very important telemedicine diagnostic evidences. High transmission delay in a bandwidth limited network becomes an intractable problem because of its large size. It’s important to achieve a quality balance between Region of Interest (ROI) and Background Region (BR) when ROI-based image encoding is being used. In this paper, a research made on balancing method of LS-SVM based ROI/BR PSNR prediction model to optimize the ROI encoding shows it’s much better than conventional methods but with very high computational complexity. We propose a new method using extreme learning machine (ELM) with lower computational complexity to improve encoding efficiency compared to LS-SVM based model. Besides, it also achieves the same effect of balancing ROI and BR.

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An Analysis of Sensor Based General Purpose Robot Programming Language

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)59968-1 ◽

1985 ◽

Vol 18 (16) ◽

pp. 239-244

Author(s):

R. Milovanovic

Keyword(s):

Programming Language ◽

General Purpose ◽

Robot Programming

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CPU AND GPU PERFORMANCE ANALYSIS ON 2D MATRIX OPERATION

Proxies : Jurnal Informatika ◽

10.24167/proxies.v2i1.3194 ◽

2021 ◽

Vol 2 (1) ◽

pp. 1

Author(s):

Kwek Benny Kurniawan ◽

YB Dwi Setianto

Keyword(s):

Graphic Processing Unit ◽

Computing Time ◽

General Purpose ◽

Parallel Processors ◽

Processing Unit ◽

Matrix Operation ◽

Industry Standard ◽

Programming Interfaces ◽

Complete Matrix ◽

Matrix Calculation

GPU or Graphic Processing Unit can be used on many platforms in general GPUs are used for rendering graphics but now GPUs are general purpose parallel processors with support for easily accessible programming interfaces and industry standard languages such as C, Python and Fortran. In this study, the authors will compare CPU and GPU for completing some matrix calculation. To compare between CPU and GPU, the authors have done some testing to observe the use of Processing Unit, memory and computing time to complete matrix calculations by changing matrix sizes and dimensions. The results of tests that have been done shows asynchronous GPU is faster than sequential. Furthermore, thread for GPU needs to be adjusted to achieve efficiency in GPU load.

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Numerical Study of an Impact Oscillator

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0256 ◽

1995 ◽

Author(s):

Kannan Marudachalam ◽

Faruk H. Bursal

Keyword(s):

Dynamical Systems ◽

Numerical Algorithm ◽

Initial Conditions ◽

Numerical Study ◽

Harmonic Excitation ◽

General Purpose ◽

Constrained Systems ◽

Global Dynamics ◽

Impact Oscillator ◽

Stick Slip

Abstract Systems with discontinuous dynamics can be found in diverse disciplines. Meshing gears with backlash, impact dampers, relative motion of components that exhibit stick-slip phenomena axe but a few examples from mechanical systems. These form a class of dynamical systems where the nonlinearity is so severe that analysis becomes formidable, especially when global behavior needs to be known. Only recently have researchers attempted to investigate such systems in terms of modern dynamical systems theory. In this work, an impact oscillator with two-sided rigid constraints is used as a paradigm for studying the characteristics of discontinuous dynamical systems. The oscillator has zero stiffness and is subjected to harmonic excitation. The system is linear without impacts. However, the impacts introduce nonlinearity and dissipation (assuming inelastic impacts). A numerical algorithm is developed for studying the global dynamics of the system. A peculiar type of solution in which the trajectories in phase space from a certain set of initial conditions merge in finite time, making the dynamics non-invertible, is investigated. Also, the effect of “grazing,” a behavior common to constrained systems, on the dynamics of the system is studied. Based on the experience gained in studying this system, the need for an efficient general-purpose numerical algorithm for solving discontinuous dynamical systems is motivated. Investigation of stress, vibration, wear, noise, etc. that are associated with impact phenomena can benefit greatly from such an algorithm.

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Moth-Flame Optimization Algorithm Based Multilevel Thresholding for Image Segmentation

International Journal of Applied Metaheuristic Computing ◽

10.4018/ijamc.2017100104 ◽

2017 ◽

Vol 8 (4) ◽

pp. 58-83 ◽

Cited By ~ 11

Author(s):

Abdul Kayom Md Khairuzzaman ◽

Saurabh Chaudhury

Keyword(s):

Image Segmentation ◽

Computational Complexity ◽

Signal To Noise Ratio ◽

Fitness Function ◽

Multilevel Thresholding ◽

Bacterial Foraging Optimization ◽

Kapur’S Entropy ◽

Moth Flame Optimization Algorithm ◽

Popular Image ◽

Better Than

Multilevel thresholding is a popular image segmentation technique. However, computational complexity of multilevel thresholding increases very rapidly with increasing number of thresholds. Metaheuristic algorithms are applied to reduce computational complexity of multilevel thresholding. A new method of multilevel thresholding based on Moth-Flame Optimization (MFO) algorithm is proposed in this paper. The goodness of the thresholds is evaluated using Kapur's entropy or Otsu's between class variance function. The proposed method is tested on a set of benchmark test images and the performance is compared with PSO (Particle Swarm Optimization) and BFO (Bacterial Foraging Optimization) based methods. The results are analyzed objectively using the fitness function and the Peak Signal to Noise Ratio (PSNR) values. It is found that MFO based multilevel thresholding method performs better than the PSO and BFO based methods.

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A Runtime System for XML Transformations in Java

BRICS Report Series ◽

10.7146/brics.v11i33.21858 ◽

2004 ◽

Vol 11 (33) ◽

Author(s):

Aske Simon Christensen ◽

Christian Kirkegaard ◽

Anders Møller

Keyword(s):

Static Analysis ◽

Programming Language ◽

Program Analysis ◽

Companion Paper ◽

General Purpose ◽

Runtime System ◽

Xml Documents ◽

Level Data ◽

High Level ◽

The Given

We show that it is possible to extend a general-purpose programming language with a convenient high-level data-type for manipulating XML documents while permitting (1) precise static analysis for guaranteeing validity of the constructed XML documents relative to the given DTD schemas, and (2) a runtime system where the operations can be performed efficiently. The system, named Xact, is based on a notion of immutable XML templates and uses XPath for deconstructing documents. A companion paper presents the program analysis; this paper focuses on the efficient runtime representation.

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Inverse Kinematic Solution of Robot Manipulators Using Interval Analysis

Journal of Mechanical Design ◽

10.1115/1.2826667 ◽

1998 ◽

Vol 120 (1) ◽

pp. 147-150 ◽

Cited By ~ 28

Author(s):

R. S. Rao ◽

A. Asaithambi ◽

S. K. Agrawal

Keyword(s):

Computational Complexity ◽

Numerical Algorithm ◽

Interval Analysis ◽

Inverse Kinematics ◽

Inverse Kinematic ◽

Real Numbers ◽

Computational Mathematics ◽

All Solutions ◽

Inverse Kinematics Problem ◽

Kinematic Solution

Interval analysis is a growing branch of computational mathematics where operations are carried out on intervals instead of real numbers. This paper presents the first application of this method to robotic mechanisms for the solution of inverse kinematics. As shown in this paper, it is possible to potentially compute all solutions of the inverse kinematics problem using this method. This paper describes the preliminaries of interval analysis, the numerical algorithm, the computational complexity, and illustrations with examples.

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