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An S-type singular value inclusion set for rectangular tensors.

Caili Sang1

  • 1College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou 550025 P.R. China.

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|July 7, 2017
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Summary
This summary is machine-generated.

Researchers developed a new S-type singular value inclusion set for rectangular tensors. This set provides sharper upper and lower bounds for the largest singular value of nonnegative rectangular tensors, improving upon existing methods.

Keywords:
inclusion setnonnegative tensorsrectangular tensorssingular value

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Area of Science:

  • Linear Algebra
  • Numerical Analysis
  • Tensor Computations

Background:

  • Singular values are crucial for understanding tensor properties.
  • Existing bounds for nonnegative rectangular tensors have limitations.
  • Efficient computation of tensor singular values is an active research area.

Purpose of the Study:

  • To introduce a novel S-type singular value inclusion set for rectangular tensors.
  • To derive new, sharper upper and lower bounds for the largest singular value.
  • To validate the improved bounds using numerical examples.

Main Methods:

  • Definition of an S-type singular value inclusion set.
  • Theoretical derivation of new bounds based on the inclusion set.
  • Comparison of the new bounds with existing results.
  • Numerical verification of the bounds' sharpness and accuracy.

Main Results:

  • An S-type singular value inclusion set for rectangular tensors was successfully constructed.
  • New upper and lower bounds for the largest singular value of nonnegative rectangular tensors were established.
  • The derived bounds demonstrate improved sharpness compared to previously reported results.
  • Numerical experiments confirmed the theoretical findings and the superiority of the new bounds.

Conclusions:

  • The proposed S-type singular value inclusion set offers a valuable tool for tensor analysis.
  • The new bounds provide a more accurate estimation of the largest singular value for nonnegative rectangular tensors.
  • This work contributes to the advancement of tensor computation and its applications.