The ill-conditioned cases we consider are 1) the small leading-coefficient case, 2) small leading-coefficient GCD case, 3) big leading coefficient case, and 4) approximately singular leading-coefficient case. We propose three new algorithms for computing the approximate GCDs in these cases. The first one is to stabilize the univariate PRS by avoiding the… (More)
Let F(x, u<sub>1</sub>,..., u<sub>ℓ</sub>) be a squarefree multivariate polynomial in main variable x and sub-variables u<sub>1</sub>,..., u<sub>ℓ</sub>. We say that the leading coefficient (LC) of F is singular if it vanishes at the origin of sub-variables. A representative algorithm for nonsparse multivariate polynomial GCD is the EZ-GCD… (More)
We present algorithms for multivariate GCD and approximate GCD by modifying Barnett's theorem, which is based on the LU-decomposition of Bézout matrix. Our method is suited for multivariate polynomials with large degrees. Also, we analyze ill-conditioned cases of our method. We show our method is stabler and faster than many other methods.
To test the hypothesis that elderly patients who have surgery for femoral neck fractures may have delirium not only after surgery but before surgery, we prospectively investigated the perioperative temporal profile of cognitive function in such patients. We performed the Abbreviated Mental Test (AMT) six times in each patient (on the day of admission, 3… (More)
Given polynomials with floating-point number coefficients, one can now compute the approximate GCD stably, except in ill-conditioned cases where the GCD has small or large leading coefficient/constant term. The cost is <i>O</i>(<i>m</i><sup>2</sup>), where <i>m</i> is the maximum of degrees of given polynomials. On the other hand, for polynomial with… (More)
Intraoperative monitoring of descending pathways by means of muscle evoked potential (MsEP) is a reliable method to monitor spinal cord motor function, but MsEP is readily affected by anesthetics. We monitored MsEP evoked by repetitive transcranial electrical stimulation of the motor cortex in 30 patients receiving spine surgery. Total intravenous… (More)
Lidocaine adhesive tape (Penles; Wyeth Lederle Japan, Ltd, Tokyo, Japan) is placed for pain relief prior to puncturing a vein with a needle. We investigated the optimal time interval from application of Penles to vein puncture by measuring current perception threshold (CPT) levels with a Neurometer, by which it was possible to measure the extent of nerve… (More)