Solving confluent Vandermonde systems of Hermite type

In this paper the authors develop two algorithms to solve systems of linear equations where the coefficients form a confluent Vandermonde matrix of Hermite type, or its transpose. These algorithms reduce the given system to upper triangular form by means of elementary matrix transformations. Recursive formulas to obtain the upper triangular form in an economical way are derived. Applications and numerical results are included.Algol-60 programs are appended.