Lecture#5 Ch#2 || Numerical Analysis|| Inverse of Matrix by Doo-little, Crout and Cholesky-Methods.
Topic: In this lecture I shall discuss How to find Inverse of Matrix by Doo-little, Crout and Cholesky-Methods. COURSE: NUMERICAL ANALYSIS- I||PUNJAB UNIVERSITY|| 7TH SEMESTER|| LEVEL: B.S MATHEMATICS CHAPTER # 2 Solution of System of Linear Equations. ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH ALL COURSES OF B.S MATHEMATICS 7TH SEMESTER CLICK THE LINK BELOW • B.S MATHEMATICS || 7TH SEMSETER|| PUNJAB U... ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH COMPLETE PLAY LIST OF NUMERICAL ANALYSIS- I B.S MATHEMATICS 7TH SEMESTER CLICK THE LINK BELOW • NUMERICAL ANALYSIS-I || B.S MATHEMATICS 7T... ------------------------------------------------------------------------------------------------------------------------------------------------------- This course is specially designed for students of B.S MATHEMATICS 7th semester and students doing M.SC MATHEMATICS annually from Punjab University Lahore Pakistan. ------------------------------------------------------------------------------------------------------------------------------------------------------- Number Systems and Errors Round off errors and computer arithmetic Error estimation Floating point arithmetic Solution of Non-Linear Equations Iterative methods and convergence: Bisection method, fixed point iterative method, Regula Falsi, Secant and Newton’s method Systems of Linear Equations Direct methods: Gaussian elimination method, Gauss-Jordan method, matrix inversion method, factorization (Doolittle, Crout and Cholesky) method and its various forms Iterative methods and convergence: Gauss-Jacobi method and Gauss-Seidel method Ill-condition system and condition number Eigen values and eigenvectors Power and Rayleigh quotient method Interpolation and Polynomial Approximation Difference operators Interpolation with unequal intervals: Lagrange’s interpolation formula, Newton’s divided difference formula, error in polynomial interpolation Interpolation with equal intervals: Gregory Newton forward/backward interpolation formula, error in polynomial interpolation Central difference interpolation formulae: Gauss’s forward/backward interpolation formula, Stirling’s formula, Laplace Everett’s formula, Bessel’s formula Recommended Books 1. Curtis F. Gerald and Patrick O. Wheatley, Applied Numerical Analysis, 6th edition, (Addison-Wesley Pearson Education, 2003) 2. Richard L. Burden and J. Douglas Faires, Numerical Analysis, 6th edition, (Brooks/Cole Publishing Company,1997) 3. John H. Mathews, Numerical Methods for Mathematics, 3rd edition (Prentice Hall International, 2003) 4. V. N. Vedamurthy and N. Ch. S. N. Iyenger, Numerical Methods, (Vikas Publishing House Pvt. Ltd, 2002) 5. Steven C. Chapra and Raymond P. Canale, Numerical Methods for Engineers, 3rd edition, (McGraw Hill International Edition, 1998) ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH ALL COURSES OF B.S MATHEMATICS 1ST SEMESTER CLICK ON THE LINK BELOW • B.S MATHEMATICS || 1ST SEMSETER|| PUNJAB U... ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH ALL COURSES OF B.S MATHEMATICS 2ND SEMESTER CLICK ON THE LINK BELOW • B.S MATHEMATICS || 2ND SEMSETER|| PUNJAB U... ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH ALL COURSES OF B.S MATHEMATICS 3RD SEMESTER CLICK ON THE LINK BELOW • B.S MATHEMATICS || 3RD SEMSETER|| PUNJAB U... ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH ALL COURSES OF B.S MATHEMATICS 4TH SEMESTER CLICK ON THE LINK BELOW • B.S MATHEMATICS || 4TH SEMSETER|| PUNJAB U... ------------------------------------------------------------------------------------------------------------------------------------- ------------------ TO WATCH ALL COURSES OF B.S MATHEMATICS 5TH SEMESTER CLICK ON THE LINK BELOW • B.S MATH || 5TH SEMSETER|| PUNJAB UNIVERSI... ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH ALL COURSES OF B.S MATHEMATICS 6TH SEMESTER CLICK ON THE LINK BELOW • B.S MATH || 6TH SEMSETER|| PUNJAB UNIVERSI... #Maths4U. #professorazmatali #numericalanalysis #cholesky-method