The proceedings in this volume provide reviews and discussions on the current and future developments in scientific computation, including numerical solutions of differential equations, numerical linear algebra, parallel computation and engineering applications. It contains papers by leading scientists in computational mathematics from US, Israel, Italy, China and Hong Kong.Contents: Multi-Scale Computational Methods: Research Activities (A Brandt)Some Applica-tions of the Probing Technique in Domain Decomposition (Tony F C Chan & T P Mathew)On the Free Formation of Constructing Stiffness Matrices (S-C Chen & Z-C Shi)Formal Power Series and Numerical Algorithms for Dynamical Systems (Feng Kang)A Finite Element Method for Linear Elastic Equations on Unbounded Domains (H-D Han & X-N Wu)Strategies for the Design of Parallel Algorithms (L-S Kang & Y-P Chen)Analysis of Computer-Extended Perturbation Series (Y-K Kwok)Finite Dimensional Approximation and Its Computation for Bifurcation Problems of Variational Inequalities (J-G Lei & C-L Liu)Cartesian Grids and Rotated Difference Methods for Multi-Dimensional Flow (R J LeVeque)Bifurcation with Symmetry Breaking for the Flow Between Two Concentric Rotating Spheres (K-T Li & X-Z Liu)The Corner Singularity and Boundary Layer and Computation for Hierachic Plate Method (L-K Li & I Babuska)New Trends in Preconditioned Krylov Subspace Methods (Y Saad)Parallel Multilevel B-Spline Preconditioners for the Biharmonic Problem (J-C Sun & B-K Li)Finite Element-Characteristic Method and Analysis for a Compressive Miscible Displacement Problem in Porous Media (Y-R Yuan)and other papersReadership: Applied and computational mathematicians.Key Features:Consists of 13 chapters written by renowned researchersIs self-contained, and includes an introductory chapter as well as an appendix comprising the main mathematical resultsIncludes all the main results of algebraic geometry codes and points out where further reading can be found