A continuous Jacobi-like approach to the simultaneous reduction of real matrices
This paper approaches the simultaneous reduction of real and complex matrices in a novel way. Any number of matrices can be considered in this approach and nearly any desired simultaneous normal form can be specified. Specifically, the cases of orthogonal simultaneous diagonalization, that of the nearest commuting matrix pair, the orthogonal equivalence reduction and the question of the closest normal matrix are solved computationally. The QR, QZ and SVD algorithms and many others can be treated similarly. The method used models the problem of simultaneous matrix reduction by forming a differential equation and following its flow until optimally, the sum of the undesired portions of the achieved near normal matrices are minimized in a Jacobi like fashion. For each of the four treated specific problems, the paper develops a constrained optimization problem and gives several computed examples that are solved by using standard ordinary differential equation initial value problem software.
scientific article; zbMATH DE number 4199477
scientific article