One of the advantages of dual algebra is the capability to express, in elegant and compact notation, operations and transforms on geometric algebra objects. This capability proved to be useful in different areas of engineering such as kinematics, dynamics, robot vision and computer graphics. This paper addresses the problem of extending the QR and LU matrix decompositions to dual numbers. The results herein presented are based on the solution of Sylvester type of linear matrix equations. The need of new variable types or overload operators is avoided. Only standard linear algebra library routines are required.
Cirelli, M., Pennestrì, E., Salvini, P., Valentini, P.p., Sinatra, R. (2019). LU and QR Matrix Decompositions in Clifford Algebra. In Proceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics.
LU and QR Matrix Decompositions in Clifford Algebra
Pennestrì E.;Salvini P.;Valentini P. P.;
2019-07-01
Abstract
One of the advantages of dual algebra is the capability to express, in elegant and compact notation, operations and transforms on geometric algebra objects. This capability proved to be useful in different areas of engineering such as kinematics, dynamics, robot vision and computer graphics. This paper addresses the problem of extending the QR and LU matrix decompositions to dual numbers. The results herein presented are based on the solution of Sylvester type of linear matrix equations. The need of new variable types or overload operators is avoided. Only standard linear algebra library routines are required.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
