The importance of scaling for the Hermite bicubic collocation equations

Journal Article · Tue Jul 01 04:00:00 EDT 1986 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0907048· OSTI ID:5449226

Dyksen, W R; Rice, J R

It is well known that improper scaling of linear equations can result in catastrophic loss of accuracy from Gauss elimination. The scaling process is not well understood and the commonly used ''scaling rules'' can fail. The authors study the scaling problem for the linear equations that arise from solving elliptic partial differential equations by collocation using Hermite bicubics. They present an a priori scaling rule that is effective but not foolproof. They conclude that one should use scaled partial pivoting for such equations. They also explore the relationship between the ordering used during Gauss elimination and the underlying geometry of the elliptic problem and conjecture that this ordering must maintain the geometric integrity of the problem in order to avoid severe round-off problems.

• Research Organization: Dept. of Computer Sciences, Purdue Univ., West Lafayette, IN 47907
• OSTI ID: 5449226
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 7:3; ISSN SIJCD
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ACCURACY
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
GAUSS FUNCTION
GEOMETRY
HERMITE POLYNOMIALS
MATHEMATICS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
SCALING LAWS