A new framework for H2-optimal model reduction

<p>In this contribution, a new framework for <math><mrow><msub><mrow><mrow><mi>H</mi></mrow></mrow><mn>2</mn></msub></mrow></math>-optimal reduction is presented, motivated by the local nature of both (tangential) interpolation and <math><mrow><msub><mrow><mrow><mi>H</mi></mrow></mrow><mn>2</mn></msub></mrow></math>-optimal approximations. The main advantage is given by a decoupling of the cost of reduction from the cost of optimization, resulting in a significant speedup in <math><mrow><msub><mrow><mrow><mi>H</mi></mrow></mrow><mn>2</mn></msub></mrow></math>-optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing <math><mrow><msub><mrow><mrow><mi>H</mi></mrow></mrow><mn>2</mn></msub></mrow></math>-optimal reduced models at a far lower cost than conventional algorithms. Detailed discussions and optimality proofs are presented for applying this framework to the reduction of multiple-input, multiple-output linear dynamical systems. The paper ends with a brief discussion on how this framework could be extended to other system classes, thus indicating how this truly is a general framework for interpolatory <math><mrow><msub><mrow><mrow><mi>H</mi></mrow></mrow><mn>2</mn></msub></mrow></math> reduction.