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Speed has always been a problem in the application of inverse problem methodology in optimal design. This is largely due to the time-consuming operations involved in the computation of gradients with respect to the many parameters. With the advent of parallel computers, this is no longer a problem. The conjugate gradient and Cholesky factorization solution procedures for the computation of gradients in the optimal design of a recording head were compared. It was found that the Cholesky factorization scheme is superior to the conjugate gradient methods in inverse problems if renumbering could be done efficiently to reduce the profile storage. However, when there are limitations in storage, conjugate gradient methods with sparse storage must be used for larger matrices.