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A divide and conquer algorithm on the double dimensional inverse eigenvalue problem for Jacobi matrices
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DOI：10.1016/j.amc.2012.10.013.png)
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摘要
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This paper proposes a divide and conquer algorithm for reconstructing a 2nth order Jacobi matrix J(2n) with a given nth order leading principal submatrix J(n) and with all eigenvalues of J(2n). This algorithm needs to compute the eigenvalues of the nth order Jacobi matrix J'(n+1),(2n) and the first components of the unit eigenvectors of J'(n+1),(2n), where J'(n+1),(2n) = J(n+1),(2n) - beta(n)e(1)e(1)(T). The method needs not to reconstruct the leading principal submatrix J(n), and can avoid computing the coefficients of the characteristic polynomial for getting the eigenvalues of J(n). (C) 2012 Elsevier Inc. All rights reserved.
Keyword:
Divide and conquer algorithm
Symmetric tridiagonal matrix
Jacobi matrix
Eigenvalue problem
Inverse eigenvalue problem
Double dimension problem
期刊
IF:
3.4
论文数:
2.3W
被引数:
3.3W
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