Diagonal pivoting for partially reconstructible Cauchy-like matrices, with applications to Toeplitz-like linear equations and to boundary rational matrix interpolation problems

摘要: Abstract In an earlier paper we exploited the displacement structure of Cauchy-like matrices to derive for them a fast O ( n 2 ) implementation Gaussian elimination with partial pivoting. One application is rapid and numerically accurate solution linear systems Toeplitz-like coefficient matrices, based on fact that latter can be transformed into by using Fourier, sine, or cosine transform. However, symmetry lost in process, algorithm given not optimal Hermitian matrices. this present new symmetric diagonal pivoting show how transform obtaining algorithms are twice as those work. Numerical experiments indicate order obtain only but also methods, it advantageous explore important case which corresponding operators have nontrivial kernels; situation gives rise what call partially reconstructible introduced studied paper. We extend transformation technique generalized Schur (i.e., displacement-based implementations elimination) variety computed examples incorporation methods leads high accuracy. focused design reliable proposed other applications; particular, briefly describe they recursively solve boundary interpolation problem J -unitary rational matrix functions.