Computing the determinant and the characteristic polynomial of a matrix via solving linear systems of equations

DOI10.1016/0020-0190(88)90166-4zbMath0662.65039OpenAlexW1977980585MaRDI QIDQ1114335

Pan, Victor Y.

Publication date: 1988

Published in: Information Processing Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-0190(88)90166-4

zbMATH Keywords

computational complexityrational interpolationcharacteristic polynomialdeterminantCramer's rulep-adic lifting

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of determinants (65F40)

Related Items (6)

The shifted number system for fast linear algebra on integer matrices ⋮ On the extension of Sarrus' rule to \(n \times n\) (\(n > 3\)) matrices: development of new method for the computation of the determinant of \(4 \times 4\) matrix ⋮ Algebraic and numerical techniques for the computation of matrix determinants ⋮ Computing the sign or the value of the determinant of an integer matrix, a complexity survey. ⋮ Nearly optimal solution of rational linear systems of equations with symbolic lifting and numerical initialization ⋮ The RCH method for computing minimal polynomials of polynomial matrices

Cites Work

• Fast algorithms for rational Hermite approximation and solution of Toeplitz systems
• Fast solution of toeplitz systems of equations and computation of Padé approximants
• Exact Solution of Systems of Linear Equations with Iterative Methods
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