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Solving matrix equations in one step with cross-point resistive arrays.

Zhong Sun1, Giacomo Pedretti1, Elia Ambrosi1

  • 1Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milan, Italy.

Proceedings of the National Academy of Sciences of the United States of America
|February 21, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces in-memory computing using resistive memory devices to solve complex algebraic problems, like linear systems and matrix eigenvectors, in a single step, accelerating computations.

Keywords:
analog computingcross-point architecturein-memory computinglinear algebraresistive memory

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Area of Science:

  • Computer Science
  • Materials Science
  • Electrical Engineering
  • Quantum Computing

Background:

  • Conventional digital computers rely on sequential Boolean operations, demanding significant steps and memory for complex tasks like solving linear systems or differential equations.
  • In-memory computing, utilizing analog data storage and physical computation within memory devices, offers a promising approach to accelerate these advanced computational tasks.
  • Resistive memory devices present a viable platform for in-memory computing due to their analog storage capabilities.

Purpose of the Study:

  • To demonstrate that a cross-point array of resistive memory devices can directly perform complex algebraic computations.
  • To show that these computations, including solving linear systems and finding matrix eigenvectors, can be achieved in a single physical step.
  • To apply this hardware-based computation to classical computing problems such as webpage ranking and solving the Schrödinger equation.

Main Methods:

  • Utilized a cross-point array architecture with resistive memory devices.
  • Leveraged the physical properties of the circuit, specifically Ohm's and Kirchhoff's laws, for computation.
  • Implemented a negative feedback connection within the cross-point circuit to facilitate the computation.

Main Results:

  • Successfully demonstrated the direct solution of systems of linear equations using the resistive memory cross-point array.
  • Showcased the ability to find matrix eigenvectors directly within the hardware.
  • Achieved these complex algebraic operations in a single computational step.

Conclusions:

  • In-memory computing with resistive memory devices enables single-step solutions for challenging algebraic problems.
  • This approach significantly accelerates computations compared to conventional digital methods.
  • The demonstrated hardware computation is applicable to practical classical computing tasks, including webpage ranking and quantum mechanical equation solving.