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All Journal Jurnal Pengabdian Kepada Masyarakat Universitas Bangka Belitung AFEBI Accounting Review Berumpun: international journal of social, politics and humanities Jambura Journal of Mathematics Jurnal Matematika UNAND ACCOUNTHIK : Journal of Accounting and Finance MATHunesa: Jurnal Ilmiah Matematika Society IDEI: JURNAL EKONOMI & BISNIS
Izma Fahria
Universitas Bangka Belitung
Arts Humanities Computer Science & IT Economics, Econometrics & Finance Education Environmental Science Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics Social Sciences Other

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SCHUR DECOMPOSITION AND DCT-DST-BASED MATRIX-VECTOR MULTIPLICATION ALGORITHM FOR REAL BLOCK SKEW CIRCULANT MATRICES Euis Asriani; Izma Fahria; Ineu Sulistiana; Reni Humairah
Jurnal Matematika UNAND Vol. 15 No. 3 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.3.358-370.2026

Abstract

Real block skew circulant matrices appear in structured linear systems and signal processing, where their algebraic properties can be exploited to design efficient numerical algorithms. This paper develops a Schur decomposition specifically for real block skew circulant matrices and proves that they can be block diagonalized via an orthogonal similarity transformation constructed from discrete cosine and discrete sine transform matrices. The resulting Schur form consists of low dimensional independent blocks, enabling a fast matrix-vector multiplication scheme based on DCT-DST operations rather than direct computation. A complexity analysis shows that the proposed approach reduces arithmetic cost while preserving numerical stability due to the orthogonality of the transforms. Numerical results validate the theoretical findings and demonstrate the efficiency of the method for large scale problems.
Co-Authors Agung Samudra Anggraeni Yunita Baiq Desy Aniska Prayanti Danil Danil Darwance, Darwance Desy Ramadhanty Desy Yuliana Dalimunthe Desy Yuliana Dalimunthe Dwi Haryadi Erika Erika Erita Rosalina Euis Asriani Faisal Akbar, Muhammad Herdianti Herdianti Ineu Sulistiana Ineu Sulistiana Khilma Luthfiyaturrohmah Muhamad Al Hafiz Nicu Rahmat Adil Novendra Hidayat Reni Humairah Ririn Amelia Rolenci Rolenci Sri Ulina Kaban Wenni Anggita, Wenni