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On a cubically convergent iterative method for matrix sign.

M Sharifi1, S Karimi Vanani1, F Khaksar Haghani1

  • 1Department of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, Iran.

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Summary
This summary is machine-generated.

This study introduces a novel iterative method for calculating the matrix sign function. The proposed algorithm demonstrates global convergence with a cubic rate, offering an efficient approach for matrix computations.

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Area of Science:

  • Numerical analysis
  • Linear algebra
  • Matrix computations

Background:

  • The matrix sign function is a fundamental tool in various scientific and engineering disciplines.
  • Existing methods for computing the matrix sign function may suffer from convergence issues or computational inefficiency.

Purpose of the Study:

  • To develop a robust and efficient iterative method for computing the matrix sign function.
  • To analyze the convergence properties and demonstrate the applicability of the proposed method.

Main Methods:

  • An iterative algorithm is proposed for the matrix sign function.
  • Theoretical analysis is conducted to establish the global convergence and cubic rate of the scheme.
  • Numerical examples are presented to validate the method's performance.

Main Results:

  • The proposed iterative scheme exhibits global convergence.
  • The method achieves a cubic rate of convergence, indicating rapid approximation.
  • Demonstrated applicability and efficiency through illustrative examples.

Conclusions:

  • The developed iterative method provides an effective approach for matrix sign function computation.
  • The scheme's global behavior and cubic convergence make it a valuable tool in numerical linear algebra.