Construction of H-Symmetric pentadiagonal matrices by three spectra. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Mirzaei, H.; Ghanbari, K.
• Is Part Of: Applied mathematics in science and engineering. Volume 30:Issue 1(2022)
• Page Start: 61
• Page End: 74
• Publication Date: 2022-01-02
• Subjects: Inverse eigenvalue problem -- modified Lanczos algorithm -- pentadiagonal matrix -- pseudo-symmetric -- H-Symmetric matrix; 15A18 -- 65F18; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/17415977.2021.2022139
• Languages: English
• ISSNs: 2769-0911

Abstract

Abstract : The set of eigenvalues of a square matrix P is denoted by σ ( P ), and the set of eigenvalues of the submatrix obtained from P by deleting its first i rows and columns of P is denoted by σ i ( P ) . It is known that a symmetric pentadiagonal matrix may be constructed from σ, σ 1 and σ 2 . The pairs σ, σ 1 and σ 1, σ 2 must interlace; the construction is not unique. In this paper we solve the inverse eigenvalue problem for H-Symmetric pentadiagonal matrices, not necessarily symmetric. Using σ, σ 1, σ 2, not necessarily interlacing, and σ ( P ) may contain complex eigenvalues, we construct the solution by modified Lanczos algorithm.