Fast and Accurate Con-Eigenvalue Algorithm for Optimal Rational Approximations

Fast and Accurate Con-Eigenvalue Algorithm for Optimal Rational Approximations

Abstra t. The need to ompute small on-eigenvalues and the asso iated on-eigenve tors of positive-de nite Cau hy matri es naturally arises when onstru ting rational approximations with a (near) optimally small L error. Spe i ally, given a rational fun tion with n poles in the unit disk, a rational approximation with m ≪ n poles in the unit disk may be obtained from the mth on-eigenve tor of an n...

A Fast Algorithm for Rational Fun tion Approximations

Fast Fitting of Convolutions Using Rational Approximations

Models of response time distributions are powerful models because they capture mean response times as well as variability and asymmetry. Some of these models are expressed with a closed-form equation (e.g. the Weibull distribution). However, a large number of others are not available in closed form, including convolutions. Fitting such distributions with the likelihood method is still possible ...

Solving Burgers' Equation Using Optimal Rational Approximations

Abstra t. We solve vis ous Burger's equation using a fast and a urate algorithm referred to here as the redu tion algorithm for omputing near optimal rational approximations. Given a proper rational fun tion with n poles, the redu tion algorithm omputes (for a desired L ∞ -approximation error) a rational approximation of the same form, but with a (near) optimally small number m ≪ n of poles. Al...

A Fast Algorithm For Fast Train Palindromic Quadratic Eigenvalue Problems

In the vibration analysis of high speed trains arises such a palindromic quadratic eigenvalue problem (PQEP) (λ2AT + λQ + A)z = 0, where A, Q ∈ Cn×n have special structures: both Q and A are m ×m block matrices with each block being k × k (thus n = m × k), and Q is complex symmetric and tridiagonal block-Toeplitz, and A has only one nonzero block in the (1,m)th block position which is the same ...