Determining the Inverse of a Vandermonde Matrix Using Partial Fraction Decomposition Method

Authors

  • Feby Seru Universitas Cenderawasih
  • Herlina Datu Wetipo
  • Tiku Tandiangnga

DOI:

https://doi.org/10.20956/j.v19i2.23916

Keywords:

Selected:Vandermonde matrix, partial fraction decomposition, adjoin method, inverse

Abstract

One method that can be used to calculate the inverse of a matrix is ​​the adjoin method. In this method, the process begins by calculating the value of the determinant and adjoin of a matrix. This study discusses a method for calculating the inverse, especially on the Vandermonde matrix using partial fraction decomposition. The advantage of this method is that it can calculate the inverse of a matrix, without the need to calculate the value of the determinant and adjoin of a matrix. The steps taken are to define a rational function and then write it in the form of a partial fraction, then by using a formula to calculate the coefficient of a partial fraction, a formula is derived to calculate the inverse of the Vandermonde matrix. After obtaining the formula for calculating the inverse, then comparing the results of the inverse calculation of the Vandermonde matrix using the partial fraction decomposition method with the adjoin method. The results obtained a formula to calculate the inverse of the Vandermonde matrix, V-1=WxA. Based on the case examples given, it can be concluded that the results of the inverse calculations performed using the partial fraction decomposition method are the same as the results of the calculations performed using the adjoin method. However, the calculations performed using the partial fraction decomposition method are more effective and efficient than using the adjoin method

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References

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Published

2023-01-05

How to Cite

Seru, F., Wetipo, H. D. ., & Tandiangnga, T. . (2023). Determining the Inverse of a Vandermonde Matrix Using Partial Fraction Decomposition Method. Jurnal Matematika, Statistika Dan Komputasi, 19(2), 359-373. https://doi.org/10.20956/j.v19i2.23916

Issue

Vol. 19 No. 2 (2023): JANUARY 2023

Section

Research Articles

License

Copyright (c) 2023 Author and publisher

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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