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Numerical methods notes

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Dr, Madhava Madireddy
Dr, Madhava Madireddy

This document contains chapter summaries for mathematical modeling, approximations and round-off errors, Gauss elimination, and LU decomposition & matrix inversion. The chapter on Gauss elimination describes a technique for solving simultaneous linear algebraic equations by combining equations to eliminate unknowns. It remains an important algorithm today and is the basis for linear equation solving in popular software packages.

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CHAPTER-1 MATHEMATICAL MODELING &ENGINEERING PROBLEM SOLVING
CHAPTER – APPROXIMATIONS &ROUND-OFFERRORS
CHAPTER – GAUSS ELIMINATION Thischapter dealswithsimultaneouslinearalgebraicequationsthatcanbe represented Generallyas a11x1 +a12x2 + . . . + a1nxn = b1 a21x1 + a22x2 + . . . + a2nxn = b2 an1x1 + an2x2 + . . . + annxn = bn where the a’sare constantcoefficientsandthe b’sare constants. The technique describedinthischapteriscalled gausselimination because itinvolves Combiningequationstoeliminateunknowns.Althoughitisone of the earliestmethodfor Solvingsimultaneousequations,itremainsamongthe mostimportantalgorithmsinuse today Andis the basisforlinerequationsolvingonmanypopularsoftware packages.
CHAPTER- LU DECOMPOSITION &MATRIXINVERSION
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes
Numerical methods notes

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Numerical methods notes

  • 1. CHAPTER-1 MATHEMATICAL MODELING &ENGINEERING PROBLEM SOLVING
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. CHAPTER – APPROXIMATIONS &ROUND-OFFERRORS
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20. CHAPTER – GAUSS ELIMINATION Thischapter dealswithsimultaneouslinearalgebraicequationsthatcanbe represented Generallyas a11x1 +a12x2 + . . . + a1nxn = b1 a21x1 + a22x2 + . . . + a2nxn = b2 an1x1 + an2x2 + . . . + annxn = bn where the a’sare constantcoefficientsandthe b’sare constants. The technique describedinthischapteriscalled gausselimination because itinvolves Combiningequationstoeliminateunknowns.Althoughitisone of the earliestmethodfor Solvingsimultaneousequations,itremainsamongthe mostimportantalgorithmsinuse today Andis the basisforlinerequationsolvingonmanypopularsoftware packages.
  • 21.
  • 22.
  • 23.
  • 24.
  • 25.
  • 26. CHAPTER- LU DECOMPOSITION &MATRIXINVERSION