# A block tangential Lanczos method for model reduction of large-scale first and second order dynamical systems

## TL;DR

This paper introduces an adaptive block tangential Lanczos method for reducing large-scale first and second order dynamical systems, improving computational efficiency while maintaining accurate system behavior approximation.

## Contribution

The paper proposes a novel adaptive block tangential Lanczos algorithm for model reduction of large-scale MIMO systems, with new algebraic properties and demonstrated effectiveness.

## Key findings

- The ABTL algorithm effectively reduces system complexity.
- Numerical experiments show high approximation accuracy.
- The method is applicable to large-scale systems with multiple inputs and outputs.

## Abstract

In this paper, we present a new approach for model reduction of large scale first and second order dynamical systems with multiple inputs and multiple outputs (MIMO). This approach is based on the projection of the initial problem onto tangential Krylov subspaces to produce a simpler reduced-order model that approximates well the behavior of the original model. We present an algorithm named: Adaptive Block Tangential Lanczos-type (ABTL) algorithm. We give some algebraic properties and present some numerical experiences to show the effectiveness of the proposed algorithms.