New convergence results and preconditioning strategies for the conjugate gradient method
Igor Kaporin · Numerical Linear Algebra with Applications · 1994
Abstract Instead of the standard estimate in terms of the spectral condition number we develop a new CG iteration number estimate depending on the quantity B = 1/ ntr M /( det M ) 1/ n , where M is an n × n preconditioned matrix. A new family of iterative methods for solving symmetric positive definite systems based on B‐reducing strategies is described. Numerical results are presented for the new algorithms and compared with several well‐known preconditioned CG methods.