Here are some of his key works:
* The Algebraic Eigenvalue Problem (1965): This book is considered a landmark work in numerical analysis and has been influential in the development of algorithms for solving eigenvalue problems.
* Rounding Errors in Algebraic Processes (1963): This book deals with the impact of rounding errors in numerical computations, particularly in the context of solving linear equations.
* The Practical Significance of the Theoretical Study of Numerical Methods (1963): This paper explores the relevance of theoretical analysis to practical numerical computations.
Beyond these, Wilkinson made significant contributions to the field through numerous research papers and his work on:
* Error analysis: He rigorously studied and quantified the errors that occur during numerical computations, especially in the context of linear algebra.
* Algorithms for solving linear equations: Wilkinson developed and refined algorithms for solving linear systems, including the QR algorithm for eigenvalue problems.
* Software development: He played a crucial role in the development of numerical software libraries, which are widely used in various scientific and engineering applications.
His work has had a profound impact on the field of numerical analysis and continues to be relevant today.