MATH 5330: Computational Methods of Linear Algebra Lecture Note 4: The Conjugate Gradient Method
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چکیده
Thus we can apply any optimization algorithm to solve this minimization problem and obtain a method for solving (1.1). At the point, let us consider the steepest descent method and select any initial guess x0. With xk available we try to find the direction along which φ(x) decreases most rapidly starting from xk and compute the next point xk+1 by minimizing φ(x) in this direction. By Taylor series expansion φ(xk +αd) =φ(xk)+α∇φ(xk)d+O(||d||) ;
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MATH 5330: Computational Methods of Linear Algebra Lecture Note 6: Conjugate Gradient Method for General Systems
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