The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covarian...The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.展开更多
To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively...To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.展开更多
Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research exten...Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research extends existing work in the literature.展开更多
文摘The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.
文摘To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.
文摘Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research extends existing work in the literature.
