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Related Concept Videos

Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
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Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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Vectors

Vectors are mathematical entities characterized by both magnitude and direction. Unlike scalars, which are defined solely by magnitude, vectors represent quantities like displacement, velocity, and force, where direction is essential. Vectors are graphically represented as directed line segments, extending from an initial point to a terminal point, denoted with bold letters or arrows placed above the symbol. Two vectors are deemed equal if they share identical magnitudes and directions,...
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In three-dimensional analytic geometry, a line can be fully described using vector equations when both a point on the line and its direction are known. This approach has practical applications in fields such as engineering and surveying, where precise spatial modeling is essential. For instance, a laser beam from a surveying instrument directed across a construction site can be modeled mathematically as a line using vectors.Let the laser beam originate from a known point P₀, represented by the...
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Related Experiment Video

Updated: Jul 8, 2026

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
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An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

Direct and implicit optical matrix-vector algorithms.

D Casasent1, A Ghosh

  • 1Carnegie-Mellon University, Department of Electrical Engineering, Pittsburgh, Pennsylvania 15213, USA.

Applied Optics
|November 15, 1983
PubMed
Summary
This summary is machine-generated.

New algorithms optimize optical matrix-vector and systolic array processors. Direct methods for linear systems and implicit methods for differential equations leverage optical processing strengths, focusing on computationally intensive matrix decomposition.

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Area of Science:

  • Computer Science
  • Optical Computing
  • Algorithm Analysis

Background:

  • Optical systolic array processors offer unique advantages for complex computations.
  • Traditional algorithms may not fully exploit the capabilities of optical processing hardware.
  • Solving linear systems and partial differential equations are computationally demanding tasks.

Purpose of the Study:

  • To introduce novel direct and implicit algorithms tailored for optical matrix-vector and systolic array processors.
  • To demonstrate how these algorithms can better utilize the inherent features of optical systolic arrays.
  • To identify and address the computationally burdensome aspects of optical computations.

Main Methods:

  • Consideration of direct algorithms for solving linear systems.
  • Exploration of implicit solutions for second-order partial differential equations.
  • Focus on matrix decomposition as a key computational task, exemplified by the Householder QR algorithm.

Main Results:

  • Direct algorithms are more suitable than indirect ones for optical linear system solutions.
  • Implicit solutions are preferred over explicit ones for optical differential equation solvers.
  • Matrix decomposition, specifically Householder QR, is identified as a critical operation for optical systems.

Conclusions:

  • Direct and implicit algorithms enhance the efficiency of optical matrix-vector and systolic array processors.
  • Focusing on matrix decomposition is crucial for optimizing optical computational tasks.
  • The proposed methods offer a pathway to more effective utilization of optical computing resources.