An extended innnite companion matrix ~ C 1 (D) and an innnite companion matrix C 1 (D) for a (nonmonic in general) matrix polynomial D is introduced and the nite companion matrix C(D) is generalized to the nonmonic case. These matrices generalize all properties of the innnite and nite companion (Frobenius) matrix corresponding to a scalar polynomial. In particular, C 1 (D) is a controllability ...

A projection method for computing the minimal eigenvalue of a symmetric and positive deenite Toeplitz matrix is presented. It generalizes and accelerates the algorithm considered in 12]. Global and cubic convergence is proved. Randomly generated test problems up to dimension 1024 demonstrate the methods good global behaviour.

The primary result in this paper is a set of O(n) time algorithms to determine whether a speci ed real, symmetric matrix is a member of any of several closely related classes: the MMA-matrices; the inverse MMA-matrices; the strictly positive, positive de nite matrices whose eigenvectors form a Soules basis; and the strictly ultrametric matrices. When the class membership question is answered in...

it is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. these conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.furthermore we introduce a new necessary and sucient condition for checkingstability of interv...

The positive semideenite constraint for the variable matrix in semideenite programming (SDP) relaxation is further relaxed by a nite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from diierent ways of expressing the positive semideenite constraint of the SDP relaxation. We present how such SOCP relaxatio...

This note summarizes a report with the same title where a study was carried out regarding a uni ed approach proposed by Kojima Mizuno and Yoshise for interior point algorithms for the linear complementarily problem with a positive semi de nite matrix This approach is extended to nonsymmetric matrices with nonnegative principal minors

Finite dynamic element methods are interpreted as Rayleigh-Ritz methods where the trial functions depend linearly on the eigenparameter. The positive eigenvalues of the corresponding cubic matrix eigenvalue problem are proved to be upper bounds of eigenvalues of the original problem which are usually better than the bounds that one gets from the corresponding nite element method.

Unlike early civilizations with an entire economy built around agriculture and the practicality of barter system, today's complex economies require immediate, low-cost transactions. The digitalization transactions is helping develop through various new assets currencies. appearance DeFi, CBDC’s, many blockchain based systems has created a bit debate among researchers. Consequently, matter maint...

Decentralized finance, powered by blockchain technology, is growing day day. This field, which emerged a few years ago, today manages $70 billion in assets. In this study, the concept of decentralized finance discussed and explained differences from traditional finance. Then, compliance with legal regulations requirements to ensure are mentioned. An evaluation has been made about financial serv...