An interpolation approach is pursued to solve a bilateral matrix polynomial equation frequently arising in control and signal processing. It results in eecient and numerically reliable resolution methods. Abstract New numerical procedures are proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal proces...

This paper considers feasible long-step primal-dual path-following methods for semidefinite programming based on Newton directions associated with central path equations of the form Φ(PXP T , P−T SP−1) − νI = 0, where the map Φ and the nonsingular matrix P satisfy several key properties. An iteration-complexity bound for the long-step method is derived in terms of an upper bound on a certain sc...

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positiv...

We consider the sparse recovery problem on Euclidean Jordan algebra (SREJA), which includes sparse signal recovery and low-rank symmetric matrix recovery as special cases. We introduce the restricted isometry property, null space property (NSP), and s-goodness for linear transformations in s-sparse element recovery on Euclidean Jordan algebra (SREJA), all of which provide sufficient conditions ...

The force regulation and inevitable positional inaccuracy of traditional control system can be compensated by the compliance/stiffness mechanism. The compliance/stiffness of a robotic mechanism is usually modeled by a 6 by 6 symmetric positive definite matrix at an equilibrium point using screw theory. When an external wrench is exerted on the mechanism and the mechanism moves away from its equ...