New generalized split Levinson and Schur algorithms for the two-dimensional linear least squares prediction problem on a polar raster are derived. The algorithms compute the prediction filter for estimating a random field at the edge of a disk, from noisy observations inside the disk. The covariance function of the random field is assumed to have a Toeplitzplus-Hankel structure for both its rad...

For computing Padé approximants, we present presumably stable recursive algorithms that follow two adjacent rows of the Padé table and generalize the well-known classical Levinson and Schur recurrences to the case of a nonnormal Padé table. Singular blocks in the table are crossed by look-ahead steps. Ill-conditioned Padé approximants are skipped also. If the size of these lookahead steps is bo...

Numerical stability of the Levinson algorithm, generalized for Toeplitz-like systems, is studied. Arguments based on the analytic results of an error analysis for floating point arithmetic produce an upper bound on the norm of the residual vector, which grows exponentially with respect to the size of the problem. The base of such an exponential function can be small for diagonally dominant Toep...

Compliment has been regarded by many as an expression to show one’s fondness and good wishes, and it is defined in the dictionary as “an expression of praise, admiration, or congratulation; a formal act of civility, courtesy or respect” (The American Heritage Dictionary, p. 302). Another definition accepted by many scholars is that “a compliment is a speech act which explicitly or implicitly at...

Since Covid19 is a contagious virus when infected, patients should follow the recommended instructions and precautions, first was to stay isolated from community as much possible. (Public Health Agency of Sweden, 2020. Although social distancing has effectively resulted in slowing virus’s spread, there are enormous challenges posed societies convince public, especially democratic countries, sta...