lsmr (least squares minimal residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. this paper presents a block version of the lsmr algorithm for solving linear systems with multiple right-hand sides. the new algorithm is based on the block bidiagonalization and derived by minimizing the frobenius norm of the resid ual matrix of normal equa...

We consider the algebraic Riccati equation for which the four coefficient matrices form an M -matrix K. When K is a nonsingular M -matrix or an irreducible singular M -matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M ...

a group g is said to be a (pf)c-group or to have polycyclic-by-finite conjugacy classes, if g/c_{g}(x^{g}) is a polycyclic-by-finite group for all xin g. this is a generalization of the familiar property of being an fc-group. de falco et al. (respectively, de giovanni and trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. ...

Minimal solutions of three-term recurrence relations can be computed accurately by various algorithms based on the theory of continued fractions . These algorithms may be adapted to computing solutions which, though not minimal, do initially behave like a minimal solution and only later, for large arguments, diverge away from the minimal solution . This note exhibits a nontrivial example of a s...

Given two languages L1 , L2 7*, we define L1hL2= [uhv | u # L1 , v # L2]. The well-known operations of catenation, right left quotient and shuffle product are examples of such operations. Other examples include the insertion and deletion operations. Recall that (see [3, 4]) given words u, v # 7*, the insertion of v into u is u v= [u1vu2 | u=u1u2] and the deletion of v from u is defined as u v=[...

osmotic dehydration, as a minimal processing method, has found increasingly wide prospects during the past few decades. this process involves mass transfer which is commonly modeled by applications of different procedures, mostly based on fick's law. in this research, we approached the modeling process by first obtaining experimental measurement of potato’s solid gain, water loss and moisture c...

Abstract We derive formulas for the minimal positive solution of a particular non-symmetric Riccati equation arising in transport theory. The formulas are based on the eigenvalues of an associated matrix. We use the formulas to explore some new properties of the minimal positive solution and to derive fast and highly accurate numerical methods. Some numerical tests demonstrate the properties of...

Background: Malignant disorder with B or T stem cell basis leads to development and continuation of acute lymphoblastic leukemia (ALL) due to aggregation of blast cells in bone marrow. The environmental, genetic, and demographic factors may influence the disease relapse. The objective of this study was to assess the relation between end of induction minimal residual disease and different risk f...