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math.NA2023
Forming a symmetric, unreduced, tridiagonal matrix with a given spectrum
Luca Dieci, Alessandro Pugliese
Given a set of distinct real numbers, our goal is to form a symmetric, unreduced, tridiagonal, matrix with those numbers as eigenvalues. We give an algorithm which is a stable…
math.NA2021★ 7 cited
Takagi factorization of matrices depending on parameters and locating degeneracies of singular values
Luca Dieci, Alessandra Papini, Alessandro Pugliese
In this work we consider the Takagi factorization of a matrix valued function depending on parameters. We give smoothness and genericity results and pay particular attention to the…
math.NA2021★ 1 cited
Decompositions and coalescing eigenvalues of symmetric definite pencils depending on parameters
Luca Dieci, Alessandra Papini, Alessandro Pugliese
In this work, we consider symmetric positive definite pencils depending on two parameters. That is, we are concerned with the generalized eigenvalue problem , where …