Parallel Inner Product-Free Algorithm for Least Squares Problems

The performance of CGLS, a basic iterative method whose main idea is to organize the computation of conjugate gradient method applied to normal equations for solving least squares problems. On modern architecture is always limited because of the global communication required for inner products. Inner products often therefore present a bottleneck, and it is desirable to reduce or even eliminate all the inner products. Following a note of B. Fischer and R. Freund 11], an inner product-free conjugate gradient-like algorithm is presented that simulates the standard conjugate gradient by approximating the conjugate gradient orthogonal polynomial by suitable chosen orthogonal polynomial from Bernstein-Szegg o class. We also apply this kind of algorithm into normal equations as CGLS to solve the least squares problems and compare the performance with the standard and modiied approaches.